College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 4 - Exponential and Logarithmic Functions - Exercise Set 4.5 - Page 507: 61


Logistic growth: growth is limited. Exponential growth$: $ growth is not limited.

Work Step by Step

Exponential growth model: $A=A_{0}e^{kt} \quad (k>0)$ (where $A_{0}$ is the initial quantity, and $A$ is the quantity after time t) The growth is unlimited, A can become arbitrarily large. ----------- The logistic growth model, given by $A=\displaystyle \frac{c}{1+ae^{-bt}}$, (a,b,c are constants and $c>0, b>0$) describes situations in which growth is limited. $y=c$ is a horizontal asymptote for the graph, and growth, $A$, can never exceed $c$.
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