Question

calculate the average rate of change from 20 to 40 minutes?
answer

Explanation:

Step1: Identify the formula for average rate of change

The formula for the average rate of change of a function \(y = f(x)\) over the interval \([x_1,x_2]\) is \(\frac{f(x_2)-f(x_1)}{x_2 - x_1}\). Here, \(x\) is time (in minutes) and \(y\) is the amount of water left in the pool (in gallons). Let \(x_1 = 20\), \(f(x_1)=60\), \(x_2 = 40\), and \(f(x_2)=20\).

Step2: Substitute the values into the formula

Substitute the values into the formula \(\frac{f(x_2)-f(x_1)}{x_2 - x_1}=\frac{20 - 60}{40-20}\).
First, calculate the numerator: \(20-60=-40\).
Then, calculate the denominator: \(40 - 20=20\).
So, \(\frac{-40}{20}=- 2\).

Answer:

\(-2\) gal per minute