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 505: 34


please see details in "work step by step"

Work Step by Step

Exponential growth model: $A=A_{0}e^{kt} \qquad(k>0)$ ($A_{0}$ is the initial quantity, $A$ is the quantity after time t). We solve for t (the time it takes for $A$ to become 3$A_{0}$). $3A_{0}=A_{0}e^{k\mathrm{r}}\displaystyle \qquad .../\times\frac{1}{A_{o}}$ $3=e^{k\mathrm{r}}\qquad .../$ take ln( ) of both sides $\mathrm{l}\mathrm{n}3 =kt$ $t=\displaystyle \frac{\ln 3}{k}$ The population will triple in $t=\displaystyle \frac{\ln 3}{k}$ years, which confirms the problem statement.
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