Answer
$\approx 600$ days
Work Step by Step
Consider the exponential growth equation as follows: $A=A_0e^{kt}$
As we are given that $A=\dfrac{1}{2} A_0$
Now, we have $(\dfrac{1}{2}) A_0=A_0e^{(139)k} \implies k =\dfrac{\ln 0.5}{(139)}$
or, $k\approx -0.00499$ years
Now, we have $A=A_0e^{kt} \implies (0.05)A_0=A_0 e^{-0.00499t}$
or, $t=\dfrac{\ln (0.05)}{-(0.00499)}$
Thus, $t\approx 600$ days
