Answer
a) $C(p) = \frac{600}{p}$
b) $\$8$ per person.
c) Domain:$2\leq p\leq 100$
Range: $6\leq C(p)\leq 300$
Work Step by Step
a) Let $C(p)$ be the cost per player in dollars and $p$ be the number of player participating in a tournament. Given that the total cost for up to $100$ players is $\$600$, the cost function can be written as \begin{equation}
C(p) = \frac{600}{p}.
\end{equation} b) Find $C(p)$ when $p= 75$.
\begin{equation}
\begin{aligned}
C(75)&= \frac{600}{75}\\
&= 8.
\end{aligned}
\end{equation} The cost per person is $\$8$ each when there are $75$ players.
c) Assume a minimum number of players participating to be $p= 2$. We are given a maximum number that can pay $\$600$ to be $100$. Now, find $C(2)$ and $C(100)$: \begin{equation}
\begin{aligned}
C(2)&= \frac{600}{2}= 300\\
C(100)&= \frac{600}{100}= 6.
\end{aligned}
\end{equation} A reasonable range and domain of the cost function would be: \begin{equation}
\begin{aligned}
\textbf{Domain:}&\quad 2\leq p\leq 100\\
\textbf{Range:}&\quad 6\leq C(p)\leq 300.
\end{aligned}
\end{equation}
