Question

A swimming pool is being filled and begins ejth 400 gallons of water in it. After 8 minutes, the pool contains 816 gallons of water. assuming that water is being poured into the pool at a constant rate, how much water will it contain after a total of 20 minutes has passed?

Answer 1

y = 52x + 400

Explanation:

A linear model has the form y = mx + b

There are two variables: the volume (y) of water and the number (x) of minutes the pool has been filling. The volume of water depends on how long the pool is filling.

m = (y₂-y₁)/(x₂ -x₁)

x₁ = 0; y₁ = 400

x₂ = 8; y₂ = 816

m = (816 - 400)/(8 - 0)

m = 416/8

m = 52 gal/min

The initial value (b) is the volume at time zero.

b = 400 gal

The linear function is

y = 52x + 400

===============

Volume after 20 min

y = 52×20 + 400

y = 1040 + 400

y = 1440 gal

The pool will contain 1440 gal in 20 min.