Question

a. about how much water was in the pool after 25 minutes? about gallons
b. approximately when were there 500 gallons of water in the pool? after about minutes
c. estimate the constant of proportionality for the number of gallons of water per minute going into the pool. about

Explanation:

Step1: Analyze the graph for part a

Locate \(x = 25\) (time in minutes) on the \(x -\)axis. Move vertically until you reach the approximate point on the graph - like pattern. Then move horizontally to the \(y -\)axis (water in gallons). The value is about \(300\) gallons.

Step2: Analyze the graph for part b

Locate \(y=500\) (water in gallons) on the \(y -\)axis. Move horizontally until you reach the approximate point on the graph - like pattern. Then move vertically to the \(x -\)axis (time in minutes). The value is about \(35\) minutes.

Step3: Calculate the constant of proportionality for part c

Take two points, say \((10,150)\) and \((20,300)\). The constant of proportionality \(k=\frac{y}{x}\). Using \((10,150)\), \(k = \frac{150}{10}=15\) (gallons per minute).

Answer:

a. \(300\)
b. \(35\)
c. \(15\)