Question

for problems 13 - 16, use the table of values to find the average rate of change over the given interval.

1. 1, 3

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function \(y = f(x)\) over the interval \([a,b]\) is \(\frac{f(b)-f(a)}{b - a}\).

Step2: Identify \(a\), \(b\), \(f(a)\) and \(f(b)\)

For the interval \([1,3]\), \(a = 1\), \(b=3\). From the table, when \(x = 1\), \(y=f(1)=40\) and when \(x = 3\), \(y = f(3)=18\).

Step3: Substitute values into the formula

Substitute \(a = 1\), \(b = 3\), \(f(a)=40\), \(f(b)=18\) into \(\frac{f(b)-f(a)}{b - a}\). We get \(\frac{18 - 40}{3-1}=\frac{- 22}{2}\).

Answer:

\(-11\)