College Algebra, Chapter 5, Review Exercise, Section Review Exercise, Problem 92

Determine how long would it take for an investment in this plan to double, if a retirement savings plan pays $4.5 \%$ interest, compounded annually.
Recall that the formula for interest compounded continuously is
$A (t) = Pe^{rt}$
If the investment is double, then $A = 2P$, so

$
\begin{equation}
\begin{aligned}
2P &= Pe ^{0.045t} && \text{Divide $P$ both sides}\\
\\
2 &= e^{0.045 t} && \text{Take ln of both sides}\\
\\
\ln 2 &= 0.045t && \text{Recall that } \ln e = 1\\
\\
t &= \frac{\ln 2}{0.045} && \text{Solve for } t\\
\\
t &= 15.40 \text{ years}
\end{aligned}
\end{equation}
$

It shows that it will take $\displaystyle 15 \frac{1}{2}$ for the investment to double.