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

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

Step-by-step 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