Answer
$\approx 15.28$ years
Work Step by Step
Consider the exponential growth equation as follows: $P=P_0e^{kt}$
As we are given that $P=0.9 P_0$
Then, we get $0.9 P_0=P_0e^{k} \implies k =\ln 0.9$
Now, when $P=\dfrac{1}{5} P_0$
Then, we get $P=(0.2) P_0$
$P=P_0e^{kt} \implies (0.2)P_0=(P_0)e^{(\ln 0.9)t}$
Thus, $t=\dfrac{\ln (0.2)}{\ln (0.9)} \approx 15.28$ years
