given the function defined in the table below, find the average rate of change, in simplest form, of the…

given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 30 ≤ x ≤ 60. x f(x) 0 7 15 10 30 13 45 16 60 19 75 22

given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 30 ≤ x ≤ 60. x f(x) 0 7 15 10 30 13 45 16 60 19 75 22

Answer

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 30$, $b = 60$, $f(a)=f(30)=13$, and $f(b)=f(60)=19$.

Step2: Substitute values into formula

$\frac{f(60)-f(30)}{60 - 30}=\frac{19 - 13}{60 - 30}$.

Step3: Simplify the expression

$\frac{19 - 13}{60 - 30}=\frac{6}{30}=\frac{1}{5}$.

Answer:

$\frac{1}{5}$