Answer
$12.6027=t$
The investment would take around 13 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:
$\frac{A(t)}{P}=2$
$r=0.055$
Also, we can transform our function as:
$A(t)=P*e^{rt}$
$\frac{A(t)}{P}=e^{rt}$
Therefore the question is to calculate $t$, such as:
$2=e^{0.055t}$
$\log_{e}2=\ln2=0.6931=0.055t$
$12.6027=t$
The investment would take around 13 years.