find the average rate of change of f(x) = 13\\sqrt{x - 8} over the interval 13, 20. write your answer as an…

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, $a = 13$, $b = 20$, and $f(x)=13\sqrt{x - 8}$.

Step2: Calculate $f(20)$

$f(20)=13\sqrt{20 - 8}=13\sqrt{12}=13\times2\sqrt{3}=26\sqrt{3}$.

Step3: Calculate $f(13)$

$f(13)=13\sqrt{13 - 8}=13\sqrt{5}$.

Step4: Compute the average rate of change

$\frac{f(20)-f(13)}{20 - 13}=\frac{26\sqrt{3}-13\sqrt{5}}{7}\approx\frac{26\times1.732 - 13\times2.236}{7}=\frac{45.032-29.068}{7}=\frac{15.964}{7}\approx2.3$.

Answer:

$2.3$