Question

A baseball team plays in a stadium that holds 51,000 spectators. With ticket prices at $10, the average attendance had been 38,000. When ticket prices were lowered to $8, the average attendance rose to 42,000. Find the demand function (price p as a function of attendance x), assuming it to be linear?? ...?

Answer 1

`p(x)=-0.0005x+29`

Explanation:

It is given that a baseball team plays in a stadium that holds 51,000 spectators.

Let x be the attendance and p be the price.

With ticket prices at $10, the average attendance had been 38,000. When ticket prices were lowered to $8, the average attendance rose to 42,000.

Assuming that the demand function is linear. It means, the demand line passes through the points (38000,10) and (42000,8).

The equation of line is

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

`y-10=(8-10)/(42000-38000)(x-38000)`

`y-10=(-2)/(4000)(x-38000)`

`y-10=-0.0005(x-38000)`

`y-10=-0.0005x-0.0005(-38000)`

`y-10=-0.0005x+19`

`y=-0.0005x+19+10`

`y=-0.0005x+29`

Substitute y=p(x).

`p(x)=-0.0005x+29`

Therefore, the demand function is
`p(x)=-0.0005x+29`.

Answer 2

To find the demand function, use the equation:
p = 10 - (x - 38000)/2000
p = 10 - x/2000 + 19
p = 29 - x/2000

This is what price p as a function of attendance x given the above information.

Thank you for posting your question. I hope that this answer helped you. Let me know if you need more help.