Answer
$15.27$ years
Work Step by Step
The amount A after t years due to a principal P
invested at an annual interest rate r, expressed as a decimal,
compounded n times per year is $A=P\displaystyle \cdot(1+\frac{r}{n})^{nt}$
If the compounding is continuous, then $A=Pe^{rt}$
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Continuous compounding: $A=Pe^{rt}$
$25,000=10,000e^{0.06t}\qquad.../\div 10,000$
$2.5=e^{0.06t}\qquad.../\ln(...)$
$\ln 2.5=0.06t$
$t=\displaystyle \frac{\ln 2.5}{0.06}\approx 15.27$ years