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Dominik [7]
3 years ago
8

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.
Mathematics
1 answer:
tino4ka555 [31]3 years ago
8 0

Answer:

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

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