Answer
$t\approx9~years$
Work Step by Step
Make $p=800$:
$800=\frac{1200}{1+3e^{-\frac{t}{5}}}$
$1+3e^{-\frac{t}{5}}=\frac{1200}{800}=1.5$
$3e^{-\frac{t}{5}}=1.5-1=0.5$
$e^{-\frac{t}{5}}=\frac{0.5}{3}$
$\ln e^{-\frac{t}{5}}=\ln\frac{0.5}{3}$
$-\frac{t}{5}=\ln\frac{0.5}{3}=\ln0.5-\ln3$
$t=5(\ln3-\ln0.5)$
$t=8.959\approx9~years$
