December 2020
Intermediate to advanced
1064 pages
49h 13m
English
Content preview from Advanced Engineering Mathematics, 7th Edition
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2.8 Nonlinear Models
INTRODUCTION
We finish our discussion of single first-order differential equations by examining some nonlinear mathematical models.
Population Dynamics
If P(t) denotes the size of a population at time t, the model for exponential growth begins with the assumption that dP/dt = kP for some k > 0. In this model the relative, or specific, growth rate defined by
(1)
is assumed to be a constant k. True cases of exponential growth over long periods of time are hard to find, because the limited resources of the environment will at ...
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