Question

find the average rate of change of $k(x)=9sqrt{x}$ over the interval $2,5$. write your answer as an integer, fraction, or decimal rounded to the nearest tenth. simplify any fractions.

Explanation:

Step1: Recall average rate - of - change formula

$\frac{k(b)-k(a)}{b - a}$, where $a = 2$, $b = 5$.

Step2: Calculate $k(2)$ and $k(5)$

$k(2)=9\sqrt{2}$, $k(5)=9\sqrt{5}$.

Step3: Substitute into formula

$\frac{9\sqrt{5}-9\sqrt{2}}{5 - 2}=\frac{9(\sqrt{5}-\sqrt{2})}{3}=3(\sqrt{5}-\sqrt{2})\approx3(2.24 - 1.41)=2.5$.

Answer:

$2.5$