Question

Part A: Which of the functions represents an exponential function? What is the common ratio of that function?Part B: What is the average rate of change for the function h(x) over the interval 2 ≤ x ≤ 4?

Answer 1

Answer:

(a)f(x), Common Ratio = 1/4

(b)-12

Explanation:

Part A

From the functions on the table, the function that represents an exponential function is f(x).

The common ratio of f(x) is derived below:

$\begin{gathered} 512\times\frac{1}{4}=128 \\ 128\times\frac{1}{4}=32 \\ 32\times\frac{1}{4}=8 \\ 8\times\frac{1}{4}=2 \end{gathered}$

The common ratio is 1/4.

Part B

We want to find the average rate of change for the function h(x) over the interval 2 ≤ x ≤ 4.

From the table:

• When x=4, h(x)=9: h(4) = 9

,

• When x=2, h(x)=33: h(2) = 33

$\begin{gathered} \text{ Average Rate of Change}=\frac{h(4)-h(2)}{4-2} \\ =\frac{9-33}{2} \\ =-\frac{24}{2} \\ =-12 \end{gathered}$

The average rate of change for h(x) over the interval 2 ≤ x ≤ 4 is -12.