Question

A football team plays in a large stadium. With a ticket price of ​$19​, the average attendance at recent games has been 50 comma 000. A market survey indicates that for each​ $1 increase in the ticket​ price, attendance decreases by 300. a. Express the number of spectators at a football​ game, N, as a function of the ticket​ price, x. b. Express the revenue from a football​ game, R, as a function of the ticket​ price, x.

Answer 1

Part 1: N(x) = 50,000 - 300(x-19)

Part 2: R(x) =-300x² + 55700x

Explanation:

Given,

The original price of each ticket = $ 19,

The original attendance = 50,000

Part 1 :

∵ For the each​ $1 increase in the ticket​ price, attendance decreases by 300.

Let x represents the price of each ticket after increment,

Thus, if price increment = (x-19) dollars,

New attendance, N(x) = 50,000 - 300(x-19)

Part 2 :

Since, revenue = price of each ticket × attendance

Thus, the revenue from the football​ game,

R(x) = x(50,000 - 300(x-19))

R(x) = 50000x - 300x²+ 5700x

⇒ R(x) =-300x² + 55700x