A football team plays in a large stadium. With a ticket price of $17 , the average attendance at recent games has been 50,000. A market survey indicates that for each $1 increase in the ticket price, attendance decreases by 200. 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. a. Write the function that expresses the number of spectators at a football game, N, as a function of the ticket price, x. Upper N (x) N (x) equals

Question

Charles Hoover

Mathematics

27 March, 23:33

A football team plays in a large stadium. With a ticket price of $17 , the average attendance at recent games has been 50,000. A market survey indicates that for each $1 increase in the ticket price, attendance decreases by 200. 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. a. Write the function that expresses the number of spectators at a football game, N, as a function of the ticket price, x. Upper N (x) N (x) equals

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Echo · Answer 1

a. N (x) = 50000 - 200x

b. R (x) = (50000-200x) (17+x)

Step-by-step explanation:

a. Given,

The the original price of each ticket = $ 17,

Also, the average attendance = 50,000

Let x be the number of times the original price of each ticket is increased by $ 1,

Also, for each $1 increase in the ticket price, attendance decreases by 200,

Thus, decrements in the attendance = 200x,

If N (x) represents the new average attendance,

Then,

N (x) = 50000 - 200x

Which is the required function,

b. Now,

Revenue = average attendance * price of each ticket

R (x) = N (x) * (17 + x)

⇒ R (x) = (50000-200x) (17+x)

Which is the required function.