Question

A local water park found that if the price of admission was $10, the attendance was about 1150 customers per dayWhen the price of admission was dropped to $6, attendance increased to about 1900 per day, Write a linear equation for the attendance in terms of the price, p. (A = mp + b)

Answer 1

Given:

a.) If the price of admission was $10, the attendance was about 1150 customers per day.

b.) When the price of admission was dropped to $6, attendance increased to about 1900 per day.

Let's generate the linear equation where:

x, y = p, A

m = slope

b = the y-intercept

We get,

Step 1: Let's determine the slope.

`\text{ m = }(y_2-y_1)/(x_2-x_1)\text{ = }(A_2-A_1)/(p_2-p_1)`
`\text{ = }\frac{\text{ 1900 - 1150}}{\text{ 6 - 10}}`
`\text{ = }\frac{\text{ 750}}{-4}`
`\text{ m = -}\frac{375\text{ }}{2}`

Step 2: Let's determine the y-intercept (b). Substitute p, A = 10, 1150 and m = -375/2 in A = mp + b

`\text{ A = mp + b}`
`\text{ 1150 = (}-(375)/(2))(10)\text{ + b}`
`\text{ 1150 = -}(3750)/(2)\text{ + b}`
`\text{ 1150 = -1875 + b}`
`\text{ b = 1150 + 1875}`
`\text{b = }3025`

Step 3: Let's complete the equation. Substitute m = -375/2 and b = 3025 in A = mp + b

`\text{ A = mp + b}`
`\text{ = (-}(375)/(2))p\text{ + (3025)}`
`\text{ A = -}(375)/(2)p\text{ + 3025}`

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

`\text{ A = -}(375)/(2)p\text{ + 3025}`