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?? ...?

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.

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erinna erinna · Answer 2 · 2020-03-28T04:25:22+01:00

Answer:

[tex]p(x)=-0.0005x+29[/tex]

Step-by-step 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

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

[tex]y-10=\dfrac{8-10}{42000-38000}(x-38000)[/tex]

[tex]y-10=\dfrac{-2}{4000}(x-38000)[/tex]

[tex]y-10=-0.0005(x-38000)[/tex]

[tex]y-10=-0.0005x-0.0005(-38000)[/tex]

[tex]y-10=-0.0005x+19[/tex]

[tex]y=-0.0005x+19+10[/tex]

[tex]y=-0.0005x+29[/tex]

Substitute y=p(x).

[tex]p(x)=-0.0005x+29[/tex]

Therefore, the demand function is [tex]p(x)=-0.0005x+29[/tex].