Answer
$$ −0.727\ \ \text{dollars per year}$$
Work Step by Step
Given $$P= 2C -18C^{-1} ,\ \ \ \ C = 9 + 3t^{−1} $$
Since $C(3)= 10$ and
\begin{align*}
\frac{dP}{dt}&= \frac{dP}{dC}\frac{dC}{dt}\\
&=( 2+18C^{-2}) (-3t^{-2})
\end{align*}
Then
\begin{align*}
\frac{dP}{dt}\bigg|_{t=3} &=( 2+18C^{-2}(3)) (-3(3)^{-2})\\
&= \left( 2+\frac{18}{100}\right) \left(\frac{-1}{3}\right)\\
&\approx −0.727\ \ \text{dollars per year}
\end{align*}
