Question

two water tanks are leaking water. the equation and the table each represent the gallons of water in the tank, y, as a function of time in minutes, x. the amount of water in tank a decreases by 11 gallons per minute. the rate of change for tank a is -11. tank a: y = 900 - 11x. tank b: (table with minutes, x: 0,1,2,3 and water in tank (gal), y: 985,975,965,955). find the rate of change for the function that represents tank b. the amount of water in tank b? by? gallons per minute. change for tank b is? (options: increases, decreases)

Explanation:

Step1: Recall the formula for rate of change

The rate of change (slope) \(m=\frac{y_2 - y_1}{x_2 - x_1}\).

Step2: Select two points from the table for Tank B

Let's take \((x_1,y_1)=(0,985)\) and \((x_2,y_2)=(1,975)\).

Step3: Calculate the rate of change

\(m=\frac{975 - 985}{1-0}=\frac{- 10}{1}=-10\).

Since the rate of change is negative, the amount of water in tank B decreases.

Answer:

The amount of water in tank B decreases by \(10\) gallons per minute. The rate of change for tank B is \(-10\).