Answer
$2.243=t$
The investment would take 2.243 years.
Work Step by Step
The future value of a continuous compound rate can be described with the following function:
$A(t)=P*e^{rt}$, where $P$ is the amount of investment at $t=0$, $r$ is the compound rate and $t$ is the time since the investment.
In this exercise:
$A(t)=700$
$P=500$
$r=0.15$
Therefore the question is to calculate $t$, such as:
$700=500*e^{0.15t}$
$\frac{7}{5}=e^{0.15t}$
$\log_{e}1.4=\ln1.4=0.3365=0.15t$
$2.243=t$
The investment would take 2.243 years.
