Question

A local cinema found that if the price of admission was $17the attendance was about 1900 customers per weekWhen the price of admission was dropped to $9. Attendance increased to about 3050 per week. Write a equation for the attendance in terms of the price. P i (A=mp+b )

Answer 1

Explanation:

From the question, A local cinema found that if the price of admission was $17the attendance was about 1900 customers per weekWhen the price of admission was dropped to $9. Attendance increased to about 3050 per week. Write a equation for the attendance in terms of the price. P i (A=mp+b )

Let price be a,and attendance, b

Attendance: 1,900 customers, when PRICE = $17

Attendance: 3,050 customers, when PRICE = $9

We then get the points,

(17, 1,900) & (9, 3,050)

Slope of linear equation,

(17,1900) (9, 3050)

find the slope m

(3050-1900)/(9 - 17)

1150/-8

-143.75=m

A=mp+b

A=-143.75p+b

using Attendance as a function of ticket price.

A(p) = mp + b

We have two points (p, A): (17, 1900), (9, 3050)

Slope: m = (2800-1500)/(7-17) = 1300/-10 = -130

A = -130p + b

Using (17, 1900) as (p, A) find b

1900 = -143.75(17) + b

1900 = -2443.75 + b

4343.75 = b

A = -143.75p + 4343.75

Answer 2

f(A)= -143.75p + 4343.75

Explanation:

Let price be x, and attendance, y

According to the given data,

admission was $17 the attendance was about 1900 customers

admission was $9 the attendance was about 3050 customers

Therefore, the points in terms of e and y coordinates would be , (17, 1900) --> (x1,y1)

& (9, 3050)---->(x2,y2)

Next is to calculate slope of linear equation i.e

m= (y2-y1)/(x2-x1)

m=(3050-1900)/(9-17)

m= -143.75

Now in order to find the equation, we use point-slope

y-y1= m (x-x1)

considering the coordinates (17, 1900) and slope -143.75

Equation becomes

y-1900 = -143.75( x- 17)

y-1900= -143.75x + 2443.75

y= -143.75x + 4343.75

or can be written as,

f(A)= -143.75p + 4343.75