Chapter 5.2, Problem 38PS

Solution

To Find: An equation that gives average cost per month as a function of the number of months of membership and the number of months after which the average cost will be $\$69$.

The required equation is $y=\frac{59x+100}{x}$ and the average cost will be $\$69$ after $10$ months.

Given information:

To join a rock-climbing gym, an initial fee of $\$100$ and a monthly fee of $\$59$ is to be paid.

Explanation:

Let the number of months of service be $x$.

The total cost for $x$ months will be, $100+59x$.

Let the average cost be $y$ . To find the average cost, divide the total cost by $x$.

  $y=\frac{59x+100}{x}$ ……… (1)

The asymptotes will be $x=0,y=59$.

The graph of the function will be

  

Calculate the value of $x$ for $y=69$ . For this substitute $y=69$ in (1),

  $\begin{array}{c}69=\frac{59x+100}{x}\\ 69x=59x+100\\ 10x=100\\ x=10\end{array}$

Therefore, the required equation is $y=\frac{59x+100}{x}$ and the average cost will be $\$69$ after $10$ months.