Given the function h(x) = 4x, Section A is from x = 0 to x = 1 and Section B is from x = 2 to x = 3.

Part A: Find the average rate of change of each section. (4 points)

Part B: How many times greater is the average rate of change of Section B than Section A? Explain why one rate of change is greater than the other. (6 points)

Average rate of change in Section A:

[tex]\dfrac{h(1)-h(0)}{1-0}=\dfrac{4-0}{1-0}=4[/tex]

Average rate of change in Section B:

[tex]\dfrac{h(3)-h(2)}{3-2}=\dfrac{12-8}{3-2}=4[/tex]

As you can see, the average rates of change are the same, as expected. [tex]h(x)=4x[/tex] is linear, which means it has a constant rate of change over any interval in its domain.

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DelcieRiveria DelcieRiveria · Answer 2 · 2018-12-28T13:27:43+01:00

Answer:

The rate of change of section A is 3 and rate of change of section B is 48.

Step-by-step explanation:

The given function is

[tex]h(x)=4^x[/tex]

Formula for average rate:

[tex]m=\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]

Section A is from x = 0 to x = 1, the average rate of change of section A is

[tex]m_1=\frac{h(1)-h(0)}{1-0}=\frac{4-1}{1}=3[/tex]

Section B is from x = 2 to x = 3, the average rate of change of section B is

[tex]m_2=\frac{h(3)-h(2)}{3-2}=\frac{64-16}{1}=48[/tex]

Therefore rate of change of section A is 3 and rate of change of section B is 48.

[tex]m_1\times k=m_2[/tex]

[tex]3\times k=48[/tex]

[tex]k=12[/tex]

Therefore average rate of change of Section B is 12 times of Section A.

The given function is an exponential function and rate of change is not constant.