question given the function defined in the table below, find the average rate of change, in simplest form…
question given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 5 ≤ x ≤ 9. x f(x) 4 4 5 8 6 16 7 32 8 64 9 128
Answer
Explanation:
Step1: Recall average - rate - of - change formula
The average rate of change of a function $y = f(x)$ over the interval $a\leq x\leq b$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 5$ and $b = 9$.
Step2: Identify $f(a)$ and $f(b)$
From the table, when $a = 5$, $f(5)=8$; when $b = 9$, $f(9)=128$.
Step3: Calculate the average rate of change
Substitute into the formula: $\frac{f(9)-f(5)}{9 - 5}=\frac{128 - 8}{4}=\frac{120}{4}=30$.
Answer:
30