# APPENDICES

B. Compound Interest and the Number *e*

1. Malthus: Population Outstrips Food Supply

5. Present Value of Lottery Winnings

7. Investing for Future: Tuition Payments

9. Verhulst: The Logistic Model

# A FITTING FORMULAS TO DATA

In this section we see how the formulas that are used in a mathematical model can be developed. Some of the formulas we use are exact. However, many formulas we use are approximations, often constructed from data.

### Fitting a Linear Function to Data

A company wants to understand the relationship between the amount spent on advertising, *a*, and total sales, *S*. The data they collect might look like that found in Table A.1.

The data in Table A.1 are linear, so a formula fits it exactly. The slope of the line is 20, and we can determine that the vertical intercept is 40, so the line is

Now suppose that the company collected the data in Table A.2. This time the ...

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