Given the function h(x) = 3(5)x, 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)

We can write the function in terms of y rather than h(x) so that:

y = 3 (5)^x

A. The rate of change is simply calculated as:

r = (y2 – y1) / (x2 – x1) where r stands for rate

Section A:

rA = [3 (5)^1 – 3 (5)^0] / (1 – 0)

rA = 12

Section B:

rB = [3 (5)^3 – 3 (5)^2] / (3 – 2)

rB = 300

B. We take the ratio of rB / rA:

rB/rA = 300 / 12

rB/rA = 25

So we see that the rate of change of section B is 25 times greater than A

step-by-step explanation:

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