In general, the average rate of change of a function f(x) from x=a to x=b is given by the formula below
[tex]A.R.C=\frac{f(b)-f(a)}{b-a}[/tex]
Thus, in our case,
[tex]A.R.C=\frac{a_3-a_2}{3-2}=a_3-a_2[/tex]
Then,
[tex]\begin{gathered} \Rightarrow A.R.C=1(3)^{3-1}-1(3)^{2-1}=3^2-3^1=9-3=6 \\ \Rightarrow A.R.C=6 \end{gathered}[/tex]
Thus, the answer is 6.
