Answer
$384$ dollars per month.
Work Step by Step
The cost function is given by, $C=0.2x^2+10,000$
Given, $\frac{dx}{dt}=12$ and $x=80$
We have to find $\frac{dC}{dt}$.
Differentiating the cost function with respect to $t$ we get,
$\frac{dC}{dt}=(0.2)(2x)\frac{dx}{dt}$
$\hspace{0.7cm}=(0.2)(2\times 80)(12)$
$\hspace{0.7cm}=384$
Therefore the rate of change of cost per month is $384$ dollars per month.
