Answer
after about $10.4$ seconds.
Work Step by Step
Solve for $t$ when $v(t)=-70$
( downwards, velocity is negative).
$80(e^{-0.2t}-1)=-70 \qquad$ ... $/\div 80$
$e^{-0.2t}-1=-\displaystyle \frac{7}{8} \qquad$ ... $/+1$
$e^{-0.2t}=\displaystyle \frac{1}{8} \qquad$ ... apply $\ln$() to both sides
$-0.2t=\displaystyle \ln(\frac{1}{8}) \qquad$ ... $/\div(-0.2)$
$t=\displaystyle \frac{\ln(\frac{1}{8})}{-0.2}\approx 10.4$ seconds.