Question

A local 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

The linear equation for the attendance in terms of the price is A = -737.5p + 3395.

Step-by-step explanation:

To write a linear equation for the attendance in terms of the price, we can use the formula A = mp + b. Here, A represents the attendance, p represents the price, m represents the slope, and b represents the y-intercept.

To find the slope, we can use the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line. Using the given information, we can calculate the slope as (2950 - 1000) / (6 - 10) = -737.5.

Now, we can substitute the slope and a point (6, 2950) into the equation to find the y-intercept:

2950 = -737.5(6) + b

b = 3395.

Thus, the linear equation for the attendance in terms of the price is A = -737.5p + 3395.