Question

this table shows values that represent an exponential function. what is the average rate of change for this function for the interval from x = 1 to x = 3? a. 4 b. 8 c. 2 d. 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 \(\frac{f(b)-f(a)}{b - a}\). Here, \(a = 1\), \(b=3\), \(f(1)=7\) and \(f(3)=13\).

Step2: Substitute the values into the formula

Substitute \(a = 1\), \(b = 3\), \(f(1)=7\) and \(f(3)=13\) into \(\frac{f(b)-f(a)}{b - a}\). We get \(\frac{13 - 7}{3-1}\).

Step3: Simplify the expression

First, calculate the numerator \(13 - 7=6\) and the denominator \(3 - 1 = 2\). Then \(\frac{6}{2}=3\).

Answer:

A. 4