Answer
$\approx 600$ days
Work Step by Step
Given: $A=\dfrac{1}{2} A_0$
The exponential growth can be written as: $A=A_0e^{kt}$ ...(1)
This implies that $\dfrac{1}{2} A_0=A_0e^{139k} \implies k =\dfrac{\ln 0.5}{139}$
or, $k\approx -0.00499$ years
Equation (1) becomes: $(0.05)A_0=A_0 e^{-0.00499t}$
$\implies t=\dfrac{\ln (0.05)}{-0.00499}$
or, $t\approx 600$ days
