Answer
$t \approx 15.27$ years
Work Step by Step
The formula for the amount $A$ after $t$ years due to a principal $P$ invested at an annual interest rate $r$ compounded $n$ times per year can be computed as:
$A=P(1+\dfrac{r}{n})^{nt}$
When the compounding is continuous, use the formula $A=Pe^{rt}$
We need to compute with continuous compounding. Thus, we use the formula: $A=Pe^{rt}$
$25,000=10,000e^{0.06t} \\2.5=e^{0.06t} \\ \ln 2.5=0.06t$
Therefore, $t= \dfrac{\ln 2.5}{0.06}\approx 15.27$ years
