QuestionFind the linear demand function for a stadium with 52,000 capacity, given ticket prices and attendance data. Write in slope-intercept form.
Studdy Solution
STEP 1
Assumptions1. The stadium holds52,000 spectators.
. With the ticket price at 6, the average attendance rose to26,000.
4. The demand function, , is linear, where is the number of spectators.
STEP 2
We are given two points on the line represented by the demand function . These points are and .
STEP 3
The slope of a line is given by the formula
STEP 4
Substitute the given points into the slope formula to find the slope of the line.
STEP 5
Calculate the slope of the line.
STEP 6
The equation of a line in slope-intercept form is , where is the slope and is the y-intercept. We can substitute the slope and one of the points into this equation to find the y-intercept.
STEP 7
olve the equation for .
STEP 8
Calculate the value of .
STEP 9
Now we have both the slope and the y-intercept, we can write the equation of the line in slope-intercept form.
So, the demand function, , is .
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