Question

Describing Function Notation of a Scenario
A swimming pool has about 603 cubic feet of water. The pool liner has a small hole and is leaking at a rate of 1.5 cubic feet each hour. Ruby wrote the equation
V(h) = -1.5h + 603 to represent the scenario. Describe what each variable represents in the function, and how they relate to each other.

Answer 1

V(h) is the volume of water in the pool (in cubic feet) after h hours.
h is the time (in hours) elapsed since the leak started.

How they relate:
- V(h) = -1.5h + 603 is a linear function: the volume decreases at a constant rate.
- The slope -1.5 means the pool loses 1.5 cubic feet of water each hour.
- The constant 603 is the initial volume when h = 0 (V(0) = 603 cubic feet).
- You can use the function to find volume after any number of hours, e.g. V(10) = -1.5(10) + 603 = 588 cubic feet.
- The pool would be empty when V(h) = 0, i.e. h = 603/1.5 = 402 hours. (Domain: 0 ≤ h ≤ 402.)