Question

An above-ground swimming pool is leaking. The function h(d) = 48 - 1. 5d gives the height of the water in the pool in inches d days after the leak began.

Part A: Evaluate h(0). Show your work. What does this value represent in the problem?
Part B: Evaluate h(5). Show your work. What does this value represent in the problem?
Part C: Write and solve an equation to determine how long it will take the pool to empty if the leak is not repaired. Explain how you set up your equation.
Part D.
Based on your answers above, should the domain for this function be restricted? If not, explain why not. If so, explain why and give the restricted domain. !!!!! Please help don’t give fake answers!!!!

Answer 1

A) 48 in : initial height of the water

B) 40.5 in : height of the water after 5 days

C) 32 days

D) Yes, should be restricted.

Domain: 0 ≤ d ≤ 32

Explanation:

`h(d) = 48 - 1. 5d`

A)

`h(0) = 48 - 1. 5(0)=48`

48 in is the initial height of the water

B)

`h(5) = 48 - 1. 5(5)=48-7.5=40.5`

40.5 in is the height of the water after 5 days

C) when the pool is empty, h = 0.

So set the equation to zero and solve for d.

`\implies 48 - 1. 5d=0\\\\\implies 1.5d=48\\\\\implies d=(48)/(1.5)\\\\\implies d=32`

D) Yes, the domain should be restricted because when d > 32, h < 0 and the height of the water in the pool cannot be negative

Domain: 0 ≤ d ≤ 32