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}$