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: 74

Answer

Doesn't make sense.

Work Step by Step

Exponential growth and decay models are given by $A=A_{0}e^{kt}$ in which $t$ represents time, $A_{0}$ is the amount present at $t=0$, and $A$ is the amount present at time $t$. If $k > 0$, the model describes growth and $k$ is the growth rate. If $k < 0$, the model describes decay and $k$ is the decay rate. ----------- Let $A_{1}=A_{0}e^{0.01t}$ be the model for growth with $ 1\%$ growth rate. and $A_{3}=A_{0}e^{0.03t}$ be the model for growth with $ 3\%$ growth rate. In 100 years time (t=100), the ratio of populations will be $\displaystyle \frac{A_{3}}{A_{1}}=\frac{A_{0}e^{0.03(100)}}{A_{0}e^{0.01(100)}}=\frac{e^{3}}{e^{1}}=e^{2}\approx$7.38905609893 so, $A_{3}\approx 7.4A_{1}$, meaning that the population with $ 3\%$ growth rate will be about 7.4 times greater than the one with $ 1\%$ growth rate.
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