Question

A local amusement park found that if the price of admission was $19, the attendance was about 1850 customers per week. When the price of admission was dropped to $11, attendance increased to about 2900 per week. Write a linear equation for the attendance in terms of the price, p. (A=mp+b)

Answer 1

A = -131.25p +4343.75

Explanation:

You want a linear equation for attendance (A) in terms of price (p), given that 1850 customers attended at a price of $19, and 2900 attended at a price of $11.

Slope

The slope of the line can be found from ...

m = (a2 -a1)/(p2 -p1)

m = (2900 -1850)/(11 -19) = 1050/-8 = -131.25

A-intercept

The value of b for the function A=mx+b can be found using ...

b = A -mx

b = 1850 -(-131.25)(19) = 4343.75

The slope-intercept form of the equation for attendance is ...

A = -131.25p +4343.75

The attachment shows these calculations and verifies the equation gives the given attendance amounts.

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