Answer
13th Month
Work Step by Step
We have $p(t)=\dfrac{1000}{1+9e^{-0.1656t}}$
Plug in $p(t)=500$
Therefore, $500=\dfrac{1000}{1+9e^{-0.1656}}$
or, $2= 1+9e^{-0.1656t}$
or, $e^{-0.1656t} =\dfrac{1}{9}$
or, $\ln e^{-0.1656t} =\ln \dfrac{1}{9}$
or, $t \approx 13$ months
