The average rate of change of a function in the interval [a,b] is given by:
[tex]m=\frac{f(b)-f(a)}{b-a}[/tex]
In this case we know that the interval is [-1,3] which means that a=-1 and b=3. This also means that we need to find f(-3) and f(-1); from the table we have:
[tex]\begin{gathered} f(-1)=\frac{1}{3} \\ f(3)=27 \end{gathered}[/tex]
Once we know all the values, we need we plug them in the expression for the average rate of change:
[tex]\begin{gathered} m=\frac{f(3)-f(-1)}{3-(-1)} \\ =\frac{27-\frac{1}{3}}{3+1} \\ =\frac{\frac{81-1}{3}}{4} \\ =\frac{\frac{80}{3}}{4} \\ =\frac{80}{12} \\ =\frac{20}{3} \\ =6.67 \end{gathered}[/tex]
Therefore, the average rate of change of the function in that interval is 6.67.
