## Intermediate Algebra: Connecting Concepts through Application

$n=3$
$40\left(\frac{4}{5}\right)^n+300=320.48$ $40\left(\frac{4}{5}\right)^n=20.48$ Divde both sides by $40$ $\left(\frac{4}{5}\right)^n=\frac{64}{125}$ Take the logarithm of both sides base $\frac{4}{5}$ and we obtain $n=\log_{\frac{4}{5}}\frac{64}{125}=3$ CHECK: $40\left(\frac{4}{5}\right)^3+300=40\left(\frac{64}{125}\right)+300=20.48+300=320.48$