Answer:
[tex] \lim_{x \to \infty} \frac{2500 + 17(x-100)}{x}=17[/tex]
Explanation:
1) Charges are:
Flat fee: 500
First 100 tickets: 20(100) = 2000
Tickets over 100: 17 ( x - 100), where x is the number of tickets.
2) Total charges: 500 + 2000 + 17(x - 100) = 2500 + 17(x - 100)
3) Average cost per ticket = total charges / number of tickets
⇒ [2500 + 17(x - 100) ] / x
4) limit as the number of tickets, x, becomes very high ⇒ x → ∞
⇒ [tex] \lim_{x \to \infty} \frac{2500 + 17(x-100)}{x} [/tex]
5) And the value of that limit is equal to 17, as shown below:
2500 / x + 17x / x - 1700/x = 0 + 17 + 0 = 17
