Answer
$16.62\text{ years}$.
Work Step by Step
The formula for continuous compounding where $r$ is the rate of interest, $t$ is the time in years is, $P$ is the principal, $A$ is the amount you get back after $t$ years:
$A=Pe^{rt}$.
Here we have:
$A=\$80000$
$P=\$25000$
$r=7\%=0.07$.
Substitute these values into the formula above to obtain:
$\$80000=\$25000 \cdot e^{0.07t}\\\frac{$80000}{\$25000}=e^{0.07t}\\3.2=e^{0.07t}\\\ln{3.2}=\ln{e^{0.07t}}\\ln{3.2}=0.07t\\\frac{ln{3.2}}{0.07}=\frac{0.07t}{0.07}\\t=\frac{ln3.2}{0.07}=16.6164\approx16.62\text{ years}$.
