Precalculus (6th Edition) Blitzer

$13.9$ years
The formula for compound interest wit $n$ compoundings per year is given by : $A= P(1+\dfrac{r}{n} )^{nt}$ Plug in the given data. $8000=4000 (1+\dfrac{0.05}{4} )^{4t}$ or, $2=(1.0125)^{4t}$ Take the log of each side. $t= \dfrac{\ln 2}{4 \ln 1.0125} \approx 13.9$ years