Answer
$
y=-13.1 x+2090
$
Work Step by Step
Find the $y$ values at $x= 50, 150$ for the linear function.
$$
\begin{aligned}
& y=5000 e^{-50 / 40}=1432.5240 . \\
& y=5000 e^{-150 / 40}=117.5887 .
\end{aligned}
$$
The slope of the line is
$$
m=\frac{q(150)-q(50)}{150-50}=\frac{117.5887-1432.524}{100}=-13.1
$$
and the $y$ intercept is
$$
\begin{aligned}
1432.5240 & =b-13.1(50) \\
b & =1432.5240+13.1(50) \\
& =1432.524+13.1(50) \\
& =2090
\end{aligned}
$$ Hence, $$
y=-13.1 x+2090
$$
