Question

Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 1\le x \le 5

1≤x≤5.

Answer 1

$$\def\arraystretch{1.5} \begin{array}{c:c} x & f(x) \\ \hline 0 & 3 \\ \hdashline 1 & 9 \\ \hdashline 2 & 27 \\ \hdashline 3 & 81 \\ \hdashline 4 & 243 \\ \hdashline 5 & 729 \\ \hdashline \end{array}$$

$$\text{average rate of change}=\dfrac{f(5)-f(1)}{5-1}$$

$$=\dfrac{729-9}{5-1}=180$$