Answer
$n=3$
Work Step by Step
$40\left(\frac{4}{5}\right)^n+300=320.48$
$40\left(\frac{4}{5}\right)^n=20.48$
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:
$40\left(\frac{4}{5}\right)^3+300=40\left(\frac{64}{125}\right)+300=20.48+300=320.48$
