Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 5 - Cumulative Test for Chapters 3-5 - Page 417: 38



Work Step by Step

$N=175e^{kt}$ $420=175e^{k8}~~$ $\frac{420}{175}=e^{8k}$ $e^{8k}=2.4$ $\ln e^{8k}=\ln2.4$ $8k=\ln2.4$ $k=\frac{\ln2.4}{8}$ The double of 420 is 840: $840=175e^{kt}~~$ $840=175e^{\frac{\ln2.4}{8}t}$ $\frac{840}{175}=e^{\frac{\ln2.4}{8}t}$ $4.8=e^{\frac{\ln2.4}{8}t}$ $\ln4.8=\ln e^{\frac{\ln2.4}{8}t}$ $\ln4.8=\frac{\ln2.4}{8}t$ $8\frac{\ln4.8}{\ln2.4}=t$ $t=14.334$ It takes $14.334-8=6.334~hours$ for the population to double the size.
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