The formula to calculate the average rate of change is given to be:
[tex]AROC=\frac{f(b)-f(a)}{b-a}[/tex]
For x = 2 and x = 5, the parameters of the function to solve with are given to be:
[tex]\begin{gathered} a=2 \\ b=5 \\ f(a)=6 \\ f(b)=21 \end{gathered}[/tex]
Therefore, the average rate of change is calculated to be:
[tex]\begin{gathered} AROC=\frac{21-6}{5-2}=\frac{15}{3} \\ AROC=5 \end{gathered}[/tex]
The average rate of change is 5.
