Question

Alocal aquarium found that if the price of admission was $10, the attendance was about 1000 customers per week. When the price of admission was dropped to $6,attendance increased to about 2950 per week. Write a linear equation for the attendance in terms of the price,p. (A = mp+b)

Answer 1

Given:

$10 price = 1000 customers per week.

$6 price = 2950 customers per week.

Let's write a linear equation for the attendance in terms of the price, p.

Apply the slope-intercept form:

y = mx + b

In this case, let's use the form:

A = mp + b

Where m is the average rate of change(slope) and b is the y-intercept.

To find the slope, m, apply the slope formula:

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

Where:

(x1, y1) ==> (10, 1000)

(x2, y2) ==> (6, 2950)

Hence, we have:

`m=(2950-1000)/(6-10)=(1950)/(-4)=-487.5`

The average rate of change is -$487.5

To find the y-intercept, b, substitute either of the points for A and p, substitute -487.5 for x then evaluate.

Let's take the first point: (10, 1000)

A = mp + b

1000 = -487.5(10) + b

1000 = -4875 + b

Add 4875 to both sides:

1000 + 4875 = -4875 + 4875 + b

5875 = b

b = 5875

Therefore, the lineart equation for the attendance in terms of the price, p is:

A = -487.5p + 5875

ANSWER:

`A=-487.5p+5875`