A baseball team plays in a stadium that holds 70,000 spectators. With the ticket price at $11, the average attendance has been 29,000. When the price dropped to $10, the average attendance rose to 35,000. Assuming the demand function, p(x)p(x), is linear, find p(x)p(x), where xx&nbsp;is the number of the spectators. Write&nbsp;p(x)p(x)&nbsp;in slope-intercept form.

Question

A baseball team plays in a stadium that holds 70,000 spectators. With the ticket price at $11, the average attendance has been 29,000. When the price dropped to $10, the average attendance rose to 35,000. Assuming the demand function, p(x)p(x), is linear, find p(x)p(x), where xx&amp;nbsp;is the number of the spectators. Write&amp;nbsp;p(x)p(x)&amp;nbsp;in slope-intercept form.

Vasquez · Accepted Answer

To solve the problem, let&#039;s use the concept of linear demand function. A linear demand function is typically expressed in slope-intercept form, which is given by:p(x)=mx+bwhere:- p(x) represents the price as a function of the number of spectators.- x represents the number of spectators.- m represents the slope of the demand function.- b represents the y-intercept of the demand function.We are given two data points:1) When the ticket price is 11, the average attendance is 29,000.2) When the ticket price is 10, the average attendance is 35,000.Let&#039;s use these two points to find the values of m and b.First, let&#039;s calculate the slope (m):m=y2−y1x2−x1where (x1,y1)=(11,29000) and (x2,y2)=(10,35000).Substituting the values, we get:m=35000−2900010−11=6000−1=−6000Now that we have the slope (m), we can substitute one of the given points and the slope into the slope-intercept form to find the y-intercept (b).Using the point (11,29000), we have:29000=(−6000)(11)+bNow, let&#039;s solve this equation for b:29000=−66000+bb=29000+66000b=95000Therefore, the demand function p(x), in slope-intercept form, is:p(x)=−6000x+95000

A baseball team plays in a stadium that

Answered question

Answer & Explanation

New Questions in College algebra