Question

A baseball team plays in a stadium that holds 56000 spectators. With the ticket price at $9 the average attendance has been 25000. When the price dropped to $7, the average attendance rose to 28000. a) Find the demand function p(x), where x is the number of the spectators. (Assume that p(x) is linear.)

Answer 1

p(x) = 38500 - 1500x.

Explanation:

The average attendance was 25000 when the ticket price at $9. The average attendance rose to 28000 when the price lowered to $7.

Therefore, if the demand function p(x) where, x is the value of each tickets is linear then we have p(9) = 25000 and p(7) = 28000.

Hence, the demand function will be given as

`(p(x) - 28000)/(28000 - 25000) = (x - 7)/(7 - 9)`

⇒ p(x) - 28000 = 1500(7 - x)

⇒ p(x) = 28000 + 10500 - 1500x

⇒ p(x) = 38500 - 1500x. (Answer)