Question

what is the average rate of change of $h(x)=2^{x + 1}$ over the interval $2,4$?

Explanation:

Step1: Find $h(4)$ and $h(2)$

First, find $h(4)$:
$h(4)=2^{4 + 1}=2^5 = 32$.
Then, find $h(2)$:
$h(2)=2^{2+1}=2^3 = 8$.

Step2: Use the average rate - of - change formula

The average rate of change of a function $y = h(x)$ over the interval $[a,b]$ is $\frac{h(b)-h(a)}{b - a}$. Here, $a = 2$, $b = 4$.
The average rate of change is $\frac{h(4)-h(2)}{4 - 2}=\frac{32 - 8}{2}$.
$\frac{32 - 8}{2}=\frac{24}{2}=12$.

Answer:

$12$