Question

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

Answer 1

Answer:

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.