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.

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

Part 2: R (x) = -300x² + 55700x

Step-by-step 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