Answer
a) $C(p)=\frac{1500}{p}$.
b) $\$ 25 $
c) Domain: $10\leq p\leq 90$
Range: $16.67\leq C(p)\leq 150$
Work Step by Step
Let $C(p)$ be the cost per person in dollars to rent the campsite and $p$ be the total number of persons in a camping group. Given that the total cost for up to $90$ people is $\$1500$, the cost function can be written as \begin{equation}
C(p) = \frac{1500}{p}.
\end{equation} b) Find $C(60)$ when $p= 60$.
\begin{equation}
\begin{aligned}
C(60)&= \frac{1500}{60}\\
&=25.
\end{aligned}
\end{equation} The cost per person is $\$25$ each when there are $60$ campers.
c) Assume a minimum number of persons in a camping group to be $p= 10$. We are given a maximum cost of $\$1500$ for up to $90$ campers. Now, find $C(10)$ and $C(90)$:
\begin{equation}
\begin{aligned}
C(10)&= \frac{1500}{10}= 150\\
C(90)&= \frac{1500}{90}\approx 16.67
\end{aligned}
\end{equation} A reasonable range and domain of the cost function would be:
\begin{equation}
\begin{aligned}
\textbf{Domain:}&\quad 10\leq p\leq 90\\
\textbf{Range:}&\quad 16.67\leq C(p)\leq 150.
\end{aligned}
\end{equation}
