College Algebra, Chapter 5, 5.4, Section 5.4, Problem 80

$v(t) = 80(1 - e^{-0.2t})$ represents the velocity of a sky diver t seconds after jumping. Determine how many seconds will it take so that the velocity will be 70 ft/s?

If $v = 70$, then


$
\begin{equation}
\begin{aligned}

70 =& 80 \left( 1 - e^{-0.2t} \right)
&& \text{Divide } 80
\\
\\
\frac{70}{80} =& \left( 1 - e^{-0.2t} \right)
&& \text{Add $e^{-0.2t}$ and subtract } \frac{70}{80}
\\
\\
e^{-0.2t} =& 1 - \frac{7}{8}
&& \text{Take $\ln$ of both sides}
\\
\\
-0.2t =& \ln \left(1 - \frac{7}{8} \right)
&& \text{Solve for } t
\\
\\
t =& 10.40 s
&&

\end{aligned}
\end{equation}
$