MATH SOLVE

4 months ago

Q:
# Describing Function Notation of a ScenarioA swimming pool has about 603 cubic feet of water. Thepool liner has a small hole and is leaking at a rate of 15cubic feet each hour Ruby wrote the equationV = -15h + 603 to represent the scenario. Describewhat each variable represents in the function, and howthey relate to each other

Accepted Solution

A:

Answer:v(h) represents the volume of the water (ft³) in the pool at h hoursh is the number of hours When h increased v(h) decreasedStep-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