find the average rate of change of k(x) = -8√(x + 18) over the interval -8,1. write your answer as an…

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = k(x)$ over the interval $[a,b]$ is $\frac{k(b)-k(a)}{b - a}$. Here, $a=-8$, $b = 1$, and $k(x)=-8\sqrt{x + 18}$.

Step2: Calculate $k(1)$

Substitute $x = 1$ into $k(x)$: $k(1)=-8\sqrt{1+18}=-8\sqrt{19}$.

Step3: Calculate $k(-8)$

Substitute $x=-8$ into $k(x)$: $k(-8)=-8\sqrt{-8 + 18}=-8\sqrt{10}$.

Step4: Calculate the average rate of change

$\frac{k(1)-k(-8)}{1-(-8)}=\frac{-8\sqrt{19}+8\sqrt{10}}{9}=\frac{8(\sqrt{10}-\sqrt{19})}{9}\approx\frac{8(3.162 - 4.359)}{9}=\frac{8\times(-1.197)}{9}=\frac{-9.576}{9}\approx - 1.1$.

Answer:

$-1.1$