given the function defined in the table below, find the average rate of char of the function over the…

given the function defined in the table below, find the average rate of char of the function over the interval 18 ≤ x ≤ 36. x f(x) 0 13 9 25 18 37 27 49 36 61

given the function defined in the table below, find the average rate of char of the function over the interval 18 ≤ x ≤ 36. x f(x) 0 13 9 25 18 37 27 49 36 61

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, $a = 18$, $b = 36$, $f(a)=f(18) = 37$, and $f(b)=f(36)=61$.

Step2: Substitute values into formula

$\frac{f(36)-f(18)}{36 - 18}=\frac{61 - 37}{36 - 18}$.

Step3: Calculate the numerator and denominator

The numerator is $61-37 = 24$, and the denominator is $36 - 18=18$. So we have $\frac{24}{18}=\frac{4}{3}$.

Answer:

$\frac{4}{3}$