Question

winona paid $135 for a lifetime membership to the zoo, so that she could gain admittance to the zoo for $1.55 per visit. write winonas average cost per visit c as a function of the number of visits when she has visited x times. what is her average cost per visit when she has visited the zoo 135 times? graph the function for x > 0. what happens to her average cost per visit if she starts when she is young and visits the zoo every day? find winonas average cost per visit c as a function of the number of visits when she has visited x times. c(x)=1.55 + \frac{135}{x} (type an expression.)

Explanation:

Step1: Identify the formula for average cost

The total cost consists of the one - time membership fee of $135$ and the cost per visit ($1.65$ per visit). So the total cost $T$ for $x$ visits is $T = 135+1.65x$. The average cost per visit $C(x)$ is the total cost divided by the number of visits $x$. So $C(x)=\frac{135 + 1.65x}{x}=1.65+\frac{135}{x}$.

Step2: Calculate average cost for $x = 135$

Substitute $x = 135$ into the function $C(x)$.
$C(135)=1.65+\frac{135}{135}$
$C(135)=1.65 + 1$
$C(135)=2.65$

Step3: Analyze the behavior as $x$ gets large

As $x$ (the number of visits) approaches infinity, the term $\frac{135}{x}$ approaches $0$ since the denominator is getting very large. So $\lim_{x
ightarrow\infty}C(x)=\lim_{x
ightarrow\infty}(1.65+\frac{135}{x})=1.65$.

Answer:

1. The average - cost function is $C(x)=1.65+\frac{135}{x}$.
2. When $x = 135$, the average cost per visit is $2.65$ dollars.
3. As the number of visits $x$ gets very large (visiting every day starting young), the average cost per visit approaches $1.65$ dollars.