## Algebra and Trigonometry 10th Edition

$6.334~hours$
$N=175e^{kt}$ $420=175e^{k8}~~$ $\frac{420}{175}=e^{8k}$ $e^{8k}=2.4$ $\ln e^{8k}=\ln2.4$ $8k=\ln2.4$ $k=\frac{\ln2.4}{8}$ 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.