Answer
$15.28$ years
Work Step by Step
Given: $P=0.9 P_0$
The exponential growth can be written as: $P=P_0e^{kt}$ ...(1)
This implies that $0.9 P_0=P_0e^{k} \implies k =\ln 0.9$
As per the given statement when $P=\dfrac{1}{5} P_0$
or, $P=0.2 P_0$
Equation (1) becomes: $0.2P_0=P_0e^{(\ln 0.9)t}$
This implies that $t=\dfrac{\ln (0.2)}{\ln (0.9)}$
or, $t\approx 15.28$ years
