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 15
cubic feet each hour Ruby wrote the equation
V = -15h + 603 to represent the scenario. Describe
what each variable represents in the function, and how
they relate to each other

Answer 1

Ruby’s function notation V(h) describes the volume of the pool after h number of hours. Hours is the independent variable and the total volume is the dependent variable.

Explanation:

sample response

Answer 2

v(h) represents the volume of the water (ft³) in the pool at h hours

h is the number of hours

When h increased v(h) decreased

Explanation:

- A swimming pool has about 603 cubic feet of water

∴ The volume of the water in the pool initially is 603 feet³

- The pool liner has a small hole and is leaking at a rate of 15 cubic

feet each hour

∴ The rate of decreasing of the volume of the water in the pool is

15 feet³ per hour

- The volume of the the water v at a time h hour can represented by

a linear function v(h)

∴ v(h) = -15 h + 603 , where v(h) is the volume of the water in the

pool in cubic feet at h hour

- Let us put an example to understand the relation between v(h)

and h

- Assume that h = 0

∵ h = 0

∴ v(0) = -15(0) + 603

∴ v(0) = 603 ft³ ⇒ The volume of the water at the beginning

- Assume that h = 2 hours, that means we need to know the volume

of the water after two hours

∵ h = 2 hours

∴ v(2) = -15(2) + 603

∴ v(2) = -30 + 603 = 573 ft³

∵ h increased from 0 to 2

∴ v(t) decreased from 603 ft³ to 573 ft³

∴ The volume decreased when the number of hours increased

* v(h) represents the volume of the water (ft³) in the pool at h hours

* h is the number of hours

* When h increased v(h) decreased