Question

given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval $5 \leq x \leq 7$.
$x$ $f(x)$
3 4
4 8
5 16
6 32
7 64
8 128
answer attempt 1 out of 2

Explanation:

Step1: Identify interval values

From the table, when $x=5$, $f(5)=16$; when $x=7$, $f(7)=64$.

Step2: Apply average rate formula

The average rate of change formula is $\frac{f(x_2)-f(x_1)}{x_2-x_1}$. Substitute $x_1=5$, $x_2=7$, $f(x_1)=16$, $f(x_2)=64$:
$\frac{64-16}{7-5}$

Step3: Calculate numerator and denominator

Compute numerator: $64-16=48$
Compute denominator: $7-5=2$

Step4: Simplify the fraction

$\frac{48}{2}=24$

Answer:

24