Answer
$10.8$ years.
Work Step by Step
The model for continuous compounding is
$A=Pe^{rt}$
We are given
$\left\{\begin{array}{l}
A=3000,\\
P=2000,\\
r=0.0375,
\end{array}\right.\qquad t=?$
We solve for $t$ as follows:
$3000=2000e^{0.0375t}$
$\displaystyle \frac{3000}{2000}=e^{0.0375t}$
$1.5=e^{0.0375t}$
$\ln 1.5=0.0375t$
$t=\displaystyle \frac{\ln 1.5}{0.0375}\approx 10.8$ years.
