book

College Algebra, 4th Edition

Name: College Algebra, 4th Edition
ISBN: 9780136747925

by J. S. Ratti, Marcus S. McWaters, Leslaw Skrzypek

January 2018

Intermediate to advanced

867 pages

40h 28m

English

Pearson

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MyLab Math Online Course for College Algebra by Ratti, McWaters, Skrzypek (access code required)
Connect the Concepts and Relate the Math
College Algebra
College Algebra
Foreword
Contents
Preface
Key Content ChangesFeatures
Get the Most Out of MyLab Math
Resources for Success
Dedication

Chapter P Basic Concepts of Algebra
Topics
Section P.1 The Real Numbers and Their Properties
Before Starting This Section, Review From Your Previous Mathematics TextsObjectivesClassifying NumbersEquality of NumbersClassifying Sets of NumbersRational NumbersSolutionPractice Problem 1Irrational NumbersSolutionPractice Problem 2Integer ExponentsSolutionPractice Problem 3The Real Number LineInequalitiesSolutionPractice Problem 4SetsDefinition of Union and IntersectionSolutionPractice Problem 5IntervalsSolutionPractice Problem 6Absolute ValueSolutionPractice Problem 7Distance Between Two Points on a Real Number LineSolutionPractice Problem 8Order of OperationsSolutionPractice Problem 9Properties of the Real NumbersSubtraction and Division of Real NumbersSolutionPractice Problem 10Algebraic ExpressionsSolutionPractice Problem 11SolutionPractice Problem 12Section P.1 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsGetting Ready for the Next Section
Section P.2 Integer Exponents and Scientific Notation
Before Starting This Section, ReviewObjectivesInteger ExponentsSolutionPractice Problem 1Rules of ExponentsSolutionPractice Problem 2SolutionPractice Problem 3SolutionPractice Problem 4SolutionPractice Problem 5SolutionPractice Problem 6Simplifying Exponential ExpressionsSolutionPractice Problem 7Scientific NotationSolutionPractice Problem 8Practice Problem 9Section P.2 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsGetting Ready for the Next Section
Section P.3 Polynomials
Before Starting This Section, ReviewObjectivesPolynomial VocabularySolutionPractice Problem 1Adding and Subtracting PolynomialsPractice Problem 2Practice Problem 3Multiplying PolynomialsPractice Problem 4Practice Problem 5Special ProductsPractice Problem 6Squaring a Binomial Sum or DifferenceSolutionPractice Problem 7The Product of the Sum and Difference of TermsSolutionPractice Problem 8SolutionPractice Problem 9Section P.3 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsGetting Ready for the Next Section
Section P.4 Factoring Polynomials
Before Starting This Section, ReviewObjectivesThe Greatest Common Monomial FactorFactoring Out a MonomialSolutionPractice Problem 1Factoring Trinomials of the Form x2+Bx+CSolutionPractice Problem 2Factoring FormulasPerfect-Square TrinomialsSolutionPractice Problem 3Difference of SquaresSolutionPractice Problem 4SolutionPractice Problem 5Difference and Sum of CubesSolutionPractice Problem 6SolutionPractice Problem 7Factoring by GroupingSolutionPractice Problem 8SolutionPractice Problem 9Factoring Trinomials of the Form Ax2+Bx+CSolutionPractice Problem 10Section P.4 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsGetting Ready for the Next Section
Section P.5 Rational Expressions
Before Starting This Section, ReviewObjectivesRational ExpressionsSolutionPractice Problem 1Lowest Terms for a Rational ExpressionSolutionPractice Problem 2Multiplication and Division of Rational ExpressionsSolutionPractice Problem 3Addition and Subtraction of Rational ExpressionsSolutionPractice Problem 4SolutionPractice Problem 5SolutionPractice Problem 6SolutionPractice Problem 7Complex FractionsSolutionPractice Problem 8SolutionPractice Problem 9Section P.5 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsGetting Ready for the Next Section
Section P.6 Rational Exponents and Radicals
Before Starting This Section, ReviewObjectivesSquare RootsSolutionPractice Problem 1Simplifying Square RootsSolutionPractice Problem 2SolutionPractice Problem 3Other RootsSolutionPractice Problem 4SolutionPractice Problem 5Like RadicalsSolutionPractice Problem 6Radicals with Different IndexesSolutionPractice Problem 7Rationalizing Radical ExpressionsSolutionPractice Problem 8ConjugatesSolutionPractice Problem 9Rational ExponentsSolutionPractice Problem 10SolutionPractice Problem 11SolutionPractice Problem 12SolutionPractice Problem 13SolutionPractice Problem 14Section P.6 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsGetting Ready for the Next Section
Chapter P Review and Tests
Review
Review Exercises
Building SkillsApplying the Concepts
Practice Test
Chapter 1 Equations and Inequalities
Topics
Section 1.1 Linear Equations in One Variable
Before Starting this Section, ReviewObjectivesDefinitionsSolutionPractice Problem 1Identities, Conditional Equations, and Inconsistent EquationsEquivalent EquationsSolving Linear Equations in One VariablePractice Problem 2SolutionPractice Problem 3SolutionPractice Problem 4SolutionPractice Problem 5SolutionPractice Problem 6FormulasSolutionPractice Problem 7SolutionPractice Problem 8SolutionPractice Problem 9Section 1.1 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsCritical Thinking/Discussion/WritingGetting Ready for the Next Section
Section 1.2 Applications of Linear Equations: Modeling
Before Starting this Section, ReviewObjectivesSolving Applied ProblemsSolutionPractice Problem 1GeometrySolutionPractice Problem 2FinanceSolutionPractice Problem 3SolutionPractice Problem 4Uniform MotionSolutionPractice Problem 5SolutionPractice Problem 6Work RateSolutionPractice Problem 7MixturesSolutionPractice Problem 8Section 1.2 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsCritical Thinking/Discussion/WritingGetting Ready for the Next Section
Section 1.3 Quadratic Equations
Before Starting this Section, ReviewObjectivesFactoring MethodSolutionPractice Problem 1SolutionPractice Problem 2SolutionPractice Problem 3The Square Root MethodSolutionPractice Problem 4Completing the SquareSolutionPractice Problem 5SolutionPractice Problem 6The Quadratic FormulaSolutionPractice Problem 7The DiscriminantSolutionPractice Problem 8ApplicationsSolutionPractice Problem 9SolutionPractice Problem 10Golden RectangleSolutionPractice Problem 11Section 1.3 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsCritical Thinking/Discussion/WritingGetting Ready for the Next Section
Section 1.4 Complex Numbers: Quadratic Equations with Complex Solutions
Before Starting this Section, ReviewObjectivesComplex NumbersSolutionPractice Problem 1Addition and SubtractionSolutionPractice Problem 2Multiplying Complex NumbersSolutionPractice Problem 3SolutionPractice Problem 4Complex Conjugates and DivisionSolutionPractice Problem 5SolutionPractice Problem 6SolutionPractice Problem 7Quadratic Equations with Complex SolutionsSolutionPractice Problem 8The DiscriminantSolutionPractice Problem 9Section 1.4 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsCritical Thinking/Writing/DiscussionGetting Ready for the Next Section
Section 1.5 Solving Other Types of Equations
Before Starting this Section, ReviewObjectivesSolving Equations by FactoringPractice Problem 1SolutionPractice Problem 2Rational EquationsSolutionPractice Problem 3SolutionPractice Problem 4Equations Involving RadicalsSolutionPractice Problem 5SolutionPractice Problem 6SolutionPractice Problem 7Equations with Rational ExponentsSolutionPractice Problem 8Equations That Are Quadratic in FormSolutionPractice Problem 9SolutionPractice Problem 10SolutionPractice Problem 11Section 1.5 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsCritical Thinking/Discussion/WritingGetting Ready for the Next Section
Section 1.6 Inequalities
Before Starting this Section, ReviewObjectivesInequalitiesLinear InequalitiesSolutionPractice Problem 1SolutionPractice Problem 2SolutionPractice Problem 3Combining Two InequalitiesSolutionPractice Problem 4SolutionPractice Problem 5SolutionPractice Problem 6SolutionPractice Problem 7SolutionPractice Problem 8Using Test Points to Solve InequalitiesPractice Problem 9Practice Problem 10Section 1.6 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsCritical Thinking/Discussion/WritingGetting Ready for the Next Section
Section 1.7 Equations and Inequalities Involving Absolute Value
Before Starting this Section, ReviewObjectivesEquations Involving Absolute ValueSolutionPractice Problem 1SolutionPractice Problem 2SolutionPractice Problem 3Inequalities Involving Absolute ValueSolutionPractice Problem 4SolutionPractice Problem 5SolutionPractice Problem 6SolutionPractice Problem 7SolutionPractice Problem 8Section 1.7 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsCritical Thinking/Discussion/WritingGetting Ready for the Next Section
Chapter 1 Review and Tests
Review
Review Exercises
Building SkillsApplying the Concepts
Practice Test A
Practice Test B
Chapter 2 Graphs and Functions
Topics
Section 2.1 The Coordinate Plane
Before Starting this Section, ReviewObjectivesThe Coordinate PlaneSolutionPractice Problem 1SolutionPractice Problem 2Scales on a Graphing UtilityDistance FormulaSolutionPractice Problem 3SolutionPractice Problem 4SolutionPractice Problem 5Midpoint FormulaSolutionPractice Problem 6Section 2.1 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsCritical Thinking / Discussion / WritingGetting Ready for the Next Section
Section 2.2 Graphs of Equations
Before Starting this Section, ReviewObjectivesGraph of an EquationSolutionPractice Problem 1CommentInterceptsSolutionPractice Problem 2SymmetrySolutionPractice Problem 3Practice Problem 4SolutionPractice Problem 5CirclesStandard FormSolutionPractice Problem 6SolutionPractice Problem 7SemicirclesGeneral FormSolutionPractice Problem 8Section 2.2 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsCritical Thinking / Discussion / WritingGetting Ready for the Next Section
Section 2.3 Lines
Before Starting this Section, ReviewObjectivesSlope of a LineSolutionInterpretationPractice Problem 1Point–Slope FormSolutionPractice Problem 2SolutionPractice Problem 3Slope–Intercept FormSolutionPractice Problem 4SolutionPractice Problem 5Equations of Horizontal and Vertical LinesSolutionPractice Problem 6General Form of the Equation of a LineSolutionPractice Problem 7SolutionPractice Problem 8Parallel and Perpendicular LinesPractice Problem 9Modeling Data Using Linear RegressionSolutionPractice Problem 10Section 2.3 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsCritical Thinking / Discussion / WritingGetting Ready for the Next Section
Section 2.4 Functions
Before Starting this Section, ReviewObjectivesFunctionsFunction NotationRepresentations of FunctionsFunctions Defined by Ordered PairsSolutionPractice Problem 1Functions Defined by Tables and GraphsFunctions Defined by EquationsSolutionPractice Problem 2SolutionPractice Problem 3SolutionPractice Problem 4The Domain of a FunctionSolutionPractice Problem 5The Range of a FunctionSolutionPractice Problem 6Graphs of FunctionsSolutionPractice Problem 7Function Information from Its GraphSolutionPractice Problem 8SolutionPractice Problem 9Building FunctionsLevel of Drugs in BloodstreamSolutionPractice Problem 10SolutionPractice Problem 11Functions in EconomicsLinear Cost FunctionLinear Price–Demand FunctionRevenue Function R(x)Profit Function P(x)SolutionPractice Problem 12Section 2.4 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsCritical Thinking / Discussion / WritingGetting Ready for the Next Section
Section 2.5 Properties of Functions
Before Starting this Section, ReviewObjectivesIncreasing and Decreasing FunctionsSolutionPractice Problem 1Relative Maximum and Minimum ValuesSolutionPractice Problem 2SolutionPractice Problem 3SolutionPractice Problem 4Even–Odd Functions and SymmetrySolutionPractice Problem 5SolutionPractice Problem 6SolutionPractice Problem 7Average Rate of ChangePractice Problem 8SolutionPractice Problem 9SolutionPractice Problem 10SolutionPractice Problem 11Section 2.5 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsCritical Thinking / Discussion / WritingGetting Ready for the Next Section
Section 2.6 A Library of Functions
Before Starting this Section, ReviewObjectivesLinear FunctionsSolutionPractice Problem 1SolutionPractice Problem 2Square Root and Cube Root FunctionsSquare Root FunctionSolutionPractice Problem 3Cube Root FunctionSolutionPractice Problem 4Piecewise FunctionsPractice Problem 5SolutionPractice Problem 6SolutionPractice Problem 7Graphing Piecewise FunctionsSolutionPractice Problem 8SolutionPractice Problem 9Basic FunctionsSection 2.6 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsCritical Thinking / Discussion / WritingGetting Ready for the Next Section
Section 2.7 Transformations of Functions
Before Starting this Section, ReviewObjectivesTransformationsVertical and Horizontal ShiftsSolutionPractice Problem 1SolutionPractice Problem 2Practice Problem 3ReflectionsComparing the Graphs of y=f(x) and y=−f(x)Comparing the Graphs of y=f(x) and y=f(−x)SolutionPractice Problem 4SolutionPractice Problem 5Stretching or CompressingComparing the Graphs of y=f(x) and y=af(x)SolutionPractice Problem 6Comparing the Graphs of y=f(x) and y=f(bx)SolutionPractice Problem 7Multiple Transformations in SequenceSolutionPractice Problem 8SolutionPractice Problem 9Section 2.7 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsCritical Thinking / Discussion / WritingGetting Ready for the Next Section
Section 2.8 Combining Functions; Composite Functions
Before Starting this Section, ReviewObjectivesCombining FunctionsSolutionPractice Problem 1SolutionPractice Problem 2Composition of FunctionsEvaluating (f∘g)(x)SolutionPractice Problem 3SolutionPractice Problem 4Domain of Composite FunctionsPractice Problem 5SolutionPractice Problem 6SolutionPractice Problem 7Decomposition of a FunctionPractice Problem 8Applications of Composite FunctionsSolutionPractice Problem 9SolutionPractice Problem 10Section 2.8 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsCritical Thinking / Discussion / WritingGetting Ready for the Next SectionSection 2.9 Inverse FunctionsBefore Starting this Section, ReviewObjectivesInversesSolutionPractice Problem 1SolutionPractice Problem 2SolutionPractice Problem 3Finding the Inverse FunctionSolutionPractice Problem 4Practice Problem 5SolutionPractice Problem 6Finding the Range of a One-to-One FunctionSolutionPractice Problem 7SolutionPractice Problem 8ApplicationsSolutionPractice Problem 9Section 2.9 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsCritical Thinking / Discussion / WritingGetting Ready for the Next Section
Chapter 2 Review and Tests
Review
Review Exercises
Building SkillsApplying the Concepts
Practice Test A
Practice Test B
Cumulative Review Exercises Chapters P–2
Chapter 3 Polynomial and Rational Functions
Topics
Section 3.1 Quadratic Functions
Before Starting this Section, ReviewObjectivesQuadratic FunctionsStandard Form of a Quadratic FunctionSolutionPractice Problem 1Practice Problem 2Graphing a Quadratic Function f(x)=ax2+bx+cConverting f(x)=ax2+bx+c to Standard FormPractice Problem 3SolutionPractice Problem 4ApplicationsSolutionPractice Problem 5SolutionPractice Problem 6Section 3.1 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsCritical Thinking / Discussion / WritingGetting Ready for the Next Section
Section 3.2 Polynomial Functions
Before Starting this Section, ReviewObjectivesPolynomial FunctionsSolutionPractice Problem 1Power FunctionsPower Function of Even DegreePower Function of Odd DegreeEnd Behavior of Polynomial FunctionsSolutionPractice Problem 2SolutionPractice Problem 3Zeros of a FunctionSolutionPractice Problem 4SolutionPractice Problem 5Zeros and Turning PointsSolutionPractice Problem 6SolutionPractice Problem 7 Turning PointsSolutionPractice Problem 8Graphing a Polynomial FunctionPractice Problem 9SolutionPractice Problem 10 Volume of a Wine BarrelSolutionPractice Problem 11Section 3.2 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsCritical Thinking / Discussion / WritingGetting Ready for the Next Section
Section 3.3 Dividing Polynomials
Before Starting this Section, ReviewObjectivesThe Division AlgorithmPractice Problem 1SolutionPractice Problem 2Synthetic DivisionPractice Problem 3SolutionPractice Problem 4The Remainder and Factor TheoremsSolutionPractice Problem 5SolutionPractice Problem 6SolutionPractice Problem 7ApplicationSolutionPractice Problem 8Section 3.3 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsCritical Thinking / Discussion / WritingGetting Ready for the Next Section
Section 3.4 The Real Zeros of a Polynomial Function
Before Starting this Section, ReviewObjectivesReal Zeros of a Polynomial FunctionRational Zeros TheoremSolutionPractice Problem 1SolutionPractice Problem 2Descartes’s Rule of SignsSolutionPractice Problem 3Bounds on the Real ZerosSolutionPractice Problem 4Find the Real Zeros of a Polynomial FunctionSolutionPractice Problem 5SolutionPractice Problem 6Section 3.4 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsCritical Thinking / Discussion / WritingGetting Ready for the Next Section
Section 3.5 The Complex Zeros of a Polynomial Function
Before Starting this Section, ReviewObjectivesSolutionPractice Problem 1Conjugate Pairs TheoremSolutionPractice Problem 2SolutionPractice Problem 3SolutionPractice Problem 4Section 3.5 ExercisesConcepts and VocabularyBuilding SkillsBeyond the BasicsCritical Thinking / Discussion / WritingGetting Ready for the Next Section
Section 3.6 Rational Functions
Before Starting this Section, ReviewObjectivesRational FunctionsSolutionPractice Problem 1Vertical and Horizontal AsymptotesTranslations of f(x)=1xSolutionPractice Problem 2SolutionPractice Problem 3SolutionPractice Problem 4SolutionPractice Problem 5Graphing Rational FunctionsPractice Problem 6SolutionPractice Problem 7SolutionPractice Problem 8Oblique AsymptotesSolutionPractice Problem 9Graph of a Revenue CurveSolutionPractice Problem 10Section 3.6 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsCritical Thinking / Discussion / WritingGetting Ready for the Next Section
Section 3.7 Variation
Before Starting this Section, ReviewObjectivesDirect VariationPractice Problem 1SolutionPractice Problem 2SolutionPractice Problem 3Inverse VariationSolutionPractice Problem 4SolutionPractice Problem 5Joint and Combined VariationSolutionPractice Problem 6Section 3.7 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsCritical Thinking / Discussion / WritingGetting Ready for the Next Section
Chapter 3 Review and Tests
Review
Review Exercises
Building SkillsApplying the Concepts
Practice Test A
Practice Test B
Cumulative Review Exercises Chapters P–3
Chapter 4 Exponential and Logarithmic Functions
Topics
Section 4.1 Exponential Functions
Before Starting this Section, ReviewObjectivesExponential FunctionsEvaluate Exponential FunctionsSolutionPractice Problem 1SolutionPractice Problem 2Graphing Exponential FunctionsSolutionPractice Problem 3Transformations on Exponential FunctionsSolutionPractice Problem 4SolutionPractice Problem 5SolutionPractice Problem 6Simple InterestSolutionPractice Problem 7Compound InterestSolutionPractice Problem 8SolutionPractice Problem 9SolutionPractice Problem 10Continuous Compound Interest FormulaContinuous CompoundingSolutionPractice Problem 11The Natural Exponential FunctionExponential Growth and DecaySolutionPractice Problem 12SolutionPractice Problem 13Section 4.1 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsCritical Thinking / Discussion / WritingGetting Ready for the Next Section
Section 4.2 Logarithmic Functions
Before Starting this Section, ReviewObjectivesLogarithmic FunctionsSolutionPractice Problem 1SolutionPractice Problem 2Evaluating LogarithmsSolutionPractice Problem 3Basic Properties of LogarithmsSolutionPractice Problem 4Domains of Logarithmic FunctionsSolutionPractice Problem 5Graphs of Logarithmic FunctionsPractice Problem 6SolutionPractice Problem 7SolutionPractice Problem 8Common LogarithmSolutionPractice Problem 9Natural LogarithmSolutionPractice Problem 10InvestmentsSolutionPractice Problem 11Newton’s Law of CoolingSolutionPractice Problem 12Section 4.2 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsCritical Thinking / Discussion / WritingGetting Ready for the Next Section
Section 4.3 Rules of Logarithms
Before Starting this Section, ReviewObjectivesRules of LogarithmsSolutionPractice Problem 1SolutionPractice Problem 2SolutionPractice Problem 3Number of DigitsSolutionPractice Problem 4Change of BaseSolutionPractice Problem 5SolutionPractice Problem 6Growth and DecayHalf-LifeSolutionPractice Problem 7Radiocarbon DatingSolutionPractice Problem 8Section 4.3 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsCritical Thinking / Discussion / WritingGetting Ready for the Next Section
Section 4.4 Exponential and Logarithmic Equations and Inequalities
Before Starting this Section, ReviewObjectivesSolving Exponential EquationsSolutionPractice Problem 1Practice Problem 2SolutionPractice Problem 3SolutionPractice Problem 4Applications of Exponential EquationsSolutionPractice Problem 5Solving Logarithmic EquationsPractice Problem 6SolutionPractice Problem 7SolutionPractice Problem 8SolutionPractice Problem 9Logarithmic and Exponential InequalitiesSolutionPractice Problem 10SolutionPractice Problem 11Section 4.4 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsCritical Thinking / Discussion / WritingGetting Ready for the Next Section
Section 4.5 Logarithmic Scales; Modeling
Before Starting this Section, ReviewObjectivespH ScaleSolutionPractice Problem 1SolutionPractice Problem 2Earthquake IntensitySolutionPractice Problem 3SolutionPractice Problem 4Energy of an EarthquakeSolutionPractice Problem 5Loudness of SoundSolutionPractice Problem 6SolutionPractice Problem 7SolutionPractice Problem 8Musical PitchSolutionPractice Problem 9SolutionPractice Problem 10Star BrightnessSolutionPractice Problem 11ModelingSolutionPractice Problem 12SolutionPractice Problem 13Section 4.5 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsGetting Ready for the Next Section
Chapter 4 Review and Tests
Review
Review Exercises
Concepts and VocabularyBuilding SkillsApplying the Concepts
Practice Test A
Practice Test B
Cumulative Review Exercises Chapters P–4
Chapter 5 Systems of Equations and Inequalities
Topics
Section 5.1 Systems of Linear Equations in Two Variables
Before Starting this Section, ReviewObjectivesSystem of EquationsSolutionPractice Problem 1Graphical MethodSolutionPractice Problem 2Substitution MethodPractice Problem 3SolutionPractice Problem 4SolutionPractice Problem 5Elimination MethodPractice Problem 6SolutionPractice Problem 7ApplicationsSolutionPractice Problem 8SolutionPractice Problem 9Section 5.1 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsCritical Thinking / Discussion / WritingGetting Ready for the Next Section
Section 5.2 Systems of Linear Equations in Three Variables
Before Starting this Section, ReviewObjectivesSystems of Linear EquationsSolutionPractice Problem 1Practice Problem 2Number of Solutions of a Linear SystemSolutionPractice Problem 3SolutionPractice Problem 4Nonsquare SystemsSolutionPractice Problem 5Geometric InterpretationAn Application to CAT ScansSolutionPractice Problem 6Section 5.2 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsCritical Thinking / Discussion / WritingGetting Ready for the Next Section
Section 5.3 Partial-Fraction Decomposition
Before Starting this Section, ReviewObjectivesPartial FractionsQ(x) Has Only Distinct Linear FactorsPractice Problem 1SolutionPractice Problem 2Q(x) Has Repeated Linear FactorsSolutionPractice Problem 3SolutionPractice Problem 4Q(x) Has Distinct Irreducible Quadratic FactorsSolutionPractice Problem 5Q(x) Has Repeated Irreducible Quadratic FactorsSolutionPractice Problem 6SolutionPractice Problem 7SolutionPractice Problem 8Section 5.3 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsCritical Thinking / Discussion / WritingGetting Ready for the Next Section
Section 5.4 Systems of Nonlinear Equations
Before Starting this Section, ReviewObjectivesSystems of Nonlinear EquationsSolving Systems of Nonlinear Equations by SubstitutionSolutionPractice Problem 1Solving Systems of Nonlinear Equations by EliminationSolutionPractice Problem 2ApplicationsSolutionPractice Problem 3Section 5.4 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsCritical Thinking / Discussion / WritingGetting Ready for the Next Section
Section 5.5 Systems of Inequalities
Before Starting this Section, ReviewObjectivesGraph of a Linear Inequality in Two VariablesSolutionPractice Problem 1Practice Problem 2SolutionPractice Problem 3 Systems of Linear Inequalities in Two VariablesSolutionPractice Problem 4SolutionPractice Problem 5Nonlinear InequalityPractice Problem 6Nonlinear SystemsSolutionPractice Problem 7Section 5.5 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsCritical Thinking / Discussion / WritingGetting Ready for the Next Section
Section 5.6 Linear Programming
Before Starting this Section, ReviewObjectivesLinear ProgrammingSolving Linear Programming ProblemsPractice Problem 1SolutionPractice Problem 2ApplicationsSolutionPractice Problem 3Section 5.6 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsCritical Thinking / Discussion / WritingGetting Ready for the Next Section
Chapter 5 Review and Tests
ReviewReview ExercisesBuilding SkillsApplying the ConceptsPractice Test APractice Test BCumulative Review Exercises Chapters P–5
Chapter 6 Matrices and Determinants
Topics
Section 6.1 Matrices and Systems of Equations
Before Starting this Section, ReviewObjectivesDefinition of a MatrixSolutionPractice Problem 1Using Matrices to Solve Linear SystemsSolutionPractice Problem 2SolutionPractice Problem 3SolutionPractice Problem 4Gaussian EliminationPractice Problem 5SolutionPractice Problem 6SolutionPractice Problem 7Gauss–Jordan EliminationSolutionPractice Problem 8SolutionPractice Problem 9SolutionPractice Problem 10Section 6.1 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsCritical Thinking/Discussion/WritingGetting Ready for the Next Section
Section 6.2 Matrix Algebra
Before Starting this Section, ReviewObjectivesEquality of MatricesSolutionPractice Problem 1Matrix Addition and Scalar MultiplicationSolutionPractice Problem 2SolutionPractice Problem 3SolutionPractice Problem 4Matrix MultiplicationSolutionPractice Problem 5SolutionPractice Problem 6SolutionPractice Problem 7SolutionPractice Problem 8SolutionPractice Problem 9 Computer GraphicsSolutionPractice Problem 10Section 6.2 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsCritical Thinking/Discussion/WritingGetting Ready for the Next Section
Section 6.3 The Matrix Inverse
Before Starting this Section, ReviewObjectivesThe Multiplicative Inverse of a MatrixSolutionPractice Problem 1SolutionPractice Problem 2Finding the Inverse of a MatrixSolutionPractice Problem 3SolutionPractice Problem 4A Rule for Finding the Inverse of a 2×2 MatrixSolutionPractice Problem 5Solving Systems of Linear Equations by Using Matrix InversesSolutionPractice Problem 6Applications of Matrix InversesThe Leontief Input–Output ModelSolutionPractice Problem 7 CryptographySolutionPractice Problem 8Section 6.3 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsCritical Thinking/Discussion/WritingGetting Ready for the Next Section
Section 6.4 Determinants and Cramer’s Rule
Before Starting this Section, ReviewObjectivesThe Determinant of a 2×2 MatrixSolutionPractice Problem 1Minors and CofactorsSolutionPractice Problem 2The Determinant of an n×n MatrixSolutionPractice Problem 3Cramer’s RuleSolutionPractice Problem 4SolutionPractice Problem 5ApplicationsSolutionPractice Problem 6Section 6.4 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsCritical Thinking/Discussion/WritingGetting Ready for the Next Section
Chapter 6 Review and Tests
Review
Review Exercises
Concepts and VocabularyApplying the Concepts
Practice Test A
Practice Test B
Cumulative Review Exercises Chapters P–6
Chapter 7 Conic Sections
Topics
Section 7.1 Conic Sections: Overview
Section 7.2 The Parabola
Before Starting this Section, ReviewObjectivesGeometric Definition of a ParabolaEquation of a ParabolaSolutionPractice Problem 1SolutionPractice Problem 2SolutionPractice Problem 3Translations of ParabolasSolutionPractice Problem 4SolutionPractice Problem 5SolutionPractice Problem 6Reflecting Property of ParabolasSolutionPractice Problem 7Section 7.2 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsCritical Thinking/Discussion/WritingGetting Ready for the Next Section
Section 7.3 The Ellipse
Before Starting this Section, ReviewObjectivesDefinition of EllipseEquation of an EllipseSolutionPractice Problem 1SolutionPractice Problem 2Translations of EllipsesSolutionPractice Problem 3SolutionPractice Problem 4SolutionPractice Problem 5ApplicationsSolutionPractice Problem 6Section 7.3 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsCritical Thinking/Discussion/WritingGetting Ready for the Next Section
Section 7.4 The Hyperbola
Before Starting this Section, ReviewObjectivesDefinition of HyperbolaSolutionPractice Problem 1SolutionPractice Problem 2SolutionPractice Problem 3The Asymptotes of a HyperbolaSolutionPractice Problem 4SolutionPractice Problem 5Graphing a Hyperbola with Center (0, 0)Practice Problem 6Translations of HyperbolasSolutionPractice Problem 7SolutionPractice Problem 8ApplicationsSolutionPractice Problem 9Section 7.4 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsCritical Thinking/Discussion/WritingGetting Ready for the Next Section
Chapter 7 Review and Tests
Review
Review Exercises
Practice Test A
Practice Test B
Cumulative Review Exercises Chapters P–7
Chapter 8 Further Topics in Algebra
Topics
Section 8.1 Sequences and Series
Before Starting this Section, ReviewObjectivesSequencesSolutionPractice Problem 1SolutionPractice Problem 2SolutionPractice Problem 3Recursive FormulasSolutionPractice Problem 4SolutionPractice Problem 5Factorial NotationSolutionPractice Problem 6SolutionPractice Problem 7Summation NotationSolutionPractice Problem 8SeriesSolutionPractice Problem 9Section 8.1 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsCritical Thinking / Discussion / WritingGetting Ready for the Next Section
Section 8.2 Arithmetic Sequences; Partial Sums
Before Starting this Section, ReviewObjectivesArithmetic SequenceSolutionPractice Problem 1SolutionPractice Problem 2SolutionPractice Problem 3SolutionPractice Problem 4Sum of a Finite Arithmetic SequenceSolutionPractice Problem 5SolutionPractice Problem 6Section 8.2 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsCritical Thinking / Discussion / WritingGetting Ready for the Next Section
Section 8.3 Geometric Sequences and Series
Before Starting this Section, ReviewObjectivesGeometric SequenceSolutionPractice Problem 1SolutionPractice Problem 2SolutionPractice Problem 3SolutionPractice Problem 4SolutionPractice Problem 5SolutionPractice Problem 6Finding the Sum of a Finite Geometric SequenceSolutionPractice Problem 7AnnuitiesSolutionPractice Problem 8Infinite Geometric SeriesSolutionPractice Problem 9SolutionPractice Problem 10Section 8.3 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsCritical Thinking / Discussion / WritingGetting Ready for the Next Section
Section 8.4 Mathematical Induction
Before Starting this Section, ReviewObjectiveMathematical InductionDetermining the Statement Pk+1 from the Statement PkSolutionPractice Problem 1SolutionPractice Problem 2SolutionPractice Problem 3Section 8.4 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsCritical Thinking / Discussion / WritingGetting Ready for the Next Section
Section 8.5 The Binomial Theorem
Before Starting this Section, ReviewObjectivesPascal’s TriangleSolutionPractice Problem 1The Binomial TheoremSolutionPractice Problem 2SolutionPractice Problem 3Binomial CoefficientsSolutionPractice Problem 4SolutionPractice Problem 5SolutionPractice Problem 6Section 8.5 ExercisesConcepts and VocabularyBuilding SkillsBeyond the BasicsCritical Thinking / Discussion / WritingGetting Ready for the Next Section
Section 8.6 Counting Principles
Before Starting this Section, ReviewObjectivesFundamental Counting PrincipleSolutionPractice Problem 1SolutionPractice Problem 2SolutionPractice Problem 3PermutationsSolutionPractice Problem 4SolutionPractice Problem 5SolutionPractice Problem 6CombinationsSolutionPractice Problem 7SolutionPractice Problem 8SolutionPractice Problem 9Distinguishable PermutationsSolutionPractice Problem 10Deciding Whether to Use Permutations, Combinations, or the Fundamental Counting PrincipleSection 8.6 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsCritical Thinking / Discussion / WritingGetting Ready for the Next Section
Section 8.7 Probability
Before Starting this Section, ReviewObjectivesThe Probability of an EventSolutionPractice Problem 1SolutionPractice Problem 2SolutionPractice Problem 3SolutionPractice Problem 4The Additive RuleMutually Exclusive EventsSolutionPractice Problem 5The Complement of an EventSolutionPractice Problem 6Experimental ProbabilitiesSolutionPractice Problem 7Section 8.7 ExercisesConcepts and VocabularyBuilding SkillsApplying the ConceptsBeyond the BasicsCritical Thinking / Discussion / Writing
Chapter 8 Review and Tests
Review
Review Exercises
Practice Test A
Practice Test B
Cumulative Review Exercises Chapters P–8
Answers
Chapter P
Section P.1
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Getting Ready for the Next Section
Section P.2
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Getting Ready for the Next Section
Section P.3
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Getting Ready for the Next Section
Section P.4
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Getting Ready for the Next Section
Section P.5
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Getting Ready for the Next Section
Section P.6
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Getting Ready for the Next Section
Review Exercises
Applying the Concepts
Practice Test
Chapter 1
Section 1.1
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking/Discussion/Writing
Getting Ready for the Next Section
Section 1.2
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking/Discussion/Writing
Getting Ready for the Next Section
Section 1.3
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Getting Ready for the Next Section
Section 1.4
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking/Discussion/Writing
Getting Ready for the Next Section
Section 1.5
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking/Discussion/Writing
Getting Ready for the Next Section
Section 1.6
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking/Discussion/Writing
Getting Ready for the Next Section
Section 1.7
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking/Discussion/Writing
Getting Ready for the Next Section
Review Exercises
Building Skills
Applying the Concepts
Practice Test A
Practice Test B
Chapter 2
Section 2.1
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 2.2
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 2.3
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 2.4
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Section 2.5
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 2.6
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 2.7
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 2.8
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 2.9
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Review Exercises
Applying the Concepts
Practice Test A
Practice Test B
Cumulative Review Exercises (Chapters P–2)
Chapter 3
Section 3.1
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Getting Ready for the Next Section
Section 3.2
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 3.3
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Getting Ready for the Next Section
Section 3.4
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Getting Ready for the Next Section
Section 3.5
Concepts and Vocabulary
Building Skills
Beyond the Basics
Critical Thinking / Discussion / Writers
Getting Ready for the Next Section
Section 3.6
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 3.7
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Review Exercises
Building Skills
Applying the Concepts
Practice Test A
Practice Test B
Cumulative Review Exercises (Chapters P–3)
Chapter 4
Section 4.1
Concepts and Vocabulary
Building Skills
Applying the Concept
Beyond the Basics
Getting Ready for the Next Section
Section 4.2
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 4.3
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 4.4
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 4.5
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Getting Ready for the Next Section
Review Exercises
Concepts and Vocabulary
Building Skills
Applying the Concepts
Practice Test A
Practice Test B
Cumulative Review Exercises (Chapters P–4)
Chapter 5
Section 5.1
Concepts and Vocabulary
Building Skills
Applying the Concepts
Getting Ready for the Next Section
Section 5.2
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 5.3
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Getting Ready for the Next Section
Section 5.4
Basic Concepts and Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 5.5
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 5.6
Basic Concepts and Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Review Exercises
Building Skills
Applying the Concepts
Practice Test A
Practice Test B
Cumulative Review Exercises (Chapters P–8)
Chapter 6
Section 6.1
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Getting Ready for the Next Section
Section 6.2
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 6.3
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 6.4
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Review Exercises
Practice Test A
Practice Test B
Cumulative Review Exercises (Chapters P–9)
Chapter 7
Section 7.2
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 7.3
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Section 7.4
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking / Discussion / Writing
Getting Ready for the Next Section
Review Exercises
Practice Test A
Practice Test B
Cumulative Review Exercises (Chapters P–7)
Chapter 8
Section 8.1
Concepts and Vocabulary
Applying the Concepts
Beyond the Basics
Critical Thinking/Discussion/Writing
Getting Ready for the Next Section
Section 8.2
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking/Discussion/Writing
Getting Ready for the Next Section
Section 8.3
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking/Discussion/Writing
Getting Ready for the Next Section
Section 8.4
Concepts and Vocabulary
Building Skills
Applying the Concepts
Getting Ready for the Next Section
Section 8.5
Concepts and Vocabulary
Building Skills
Beyond the Basics
Getting Ready for the Next Section
Section 8.6
Concepts and Vocabulary
Building Skills
Beyond the Basics
Critical Thinking/Discussion/Writing
Getting Ready for the Next Section
Section 8.7
Concepts and Vocabulary
Building Skills
Applying the Concepts
Beyond the Basics
Critical Thinking/Discussion/Writing
Review Exercises
Practice Test A
Practice Test B
Cumulative Review Exercises (Chapters P–8)
Credits
Index
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
Algebra–Formulas and Definitions
Geometry–Formulas

Content preview from College Algebra, 4th Edition

Section 4.5 Logarithmic Scales; Modeling

Before Starting this Section, Review

1 Exponential form for logarithms (Section 4.2 , page 445)
2 Properties of logarithms (Section 4.2 , page 446)
3 Rules for logarithms (Section 4.3 , page 471)

Objectives

1 Define pH.
2 Define the Richter scale for measuring earthquake intensity.
3 Define scales for measuring sound.
4 Define magnitude of star brightness.
5 Build models from data

A logarithmic scale is a scale in which logarithms are used in the measurement of quantities. Suppose we have a quantity that has a small positive range of variation (for example, from $0.00001 = 10^{- 5}$ to $0.0001 = 10^{- 4}$ ); then ...

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