find the average rate of change of g(x) = -16 / (x - 20) over the interval 12, 13. write your answer as an…

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = g(x)$ over the interval $[a,b]$ is $\frac{g(b)-g(a)}{b - a}$. Here, $a = 12$, $b = 13$, and $g(x)=\frac{-16}{x - 20}$.

Step2: Calculate $g(12)$

$g(12)=\frac{-16}{12 - 20}=\frac{-16}{-8}=2$.

Step3: Calculate $g(13)$

$g(13)=\frac{-16}{13 - 20}=\frac{-16}{-7}=\frac{16}{7}$.

Step4: Calculate the average rate of change

$\frac{g(13)-g(12)}{13 - 12}=\frac{\frac{16}{7}-2}{1}$. First, simplify $\frac{16}{7}-2=\frac{16}{7}-\frac{14}{7}=\frac{16 - 14}{7}=\frac{2}{7}$.

Answer:

$\frac{2}{7}$