Question

given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval $1 \leq x \leq 13$.
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$$\begin{tabular}{|c|c|} \\hline $x$ & $f(x)$ \\\\ \\hline 1 & 77 \\\\ \\hline 4 & 74 \\\\ \\hline 7 & 71 \\\\ \\hline 10 & 68 \\\\ \\hline 13 & 65 \\\\ \\hline \\end{tabular}$$

Explanation:

Step1: Identify interval endpoints

From the table, when $x=1$, $f(1)=77$; when $x=13$, $f(13)=65$.

Step2: Apply average rate formula

Average rate = $\frac{f(13)-f(1)}{13-1}$ = $\frac{65-77}{12}$ = $\frac{-12}{12}$ = $-1$.

Answer:

$-1$