#### Answer

$t\approx-103.972$

#### Work Step by Step

Taking the natural logarithm of both sides and using the properties of logarithms, the value of the variable that satisfies the given equation, $
e^{-0.02t}=8
,$ is
\begin{array}{l}\require{cancel}
\ln e^{-0.02t}=\ln 8
\\\\
-0.02t\ln e=\ln 8
\\\\
-0.02t(1)=\ln 8
\\\\
-0.02t=\ln 8
\\\\
t=\dfrac{\ln 8}{-0.02}
\\\\
t\approx-103.972
.\end{array}