Given the function f (x) = 4 (2) x, section a is from x = 1 to x = 2 and section b is from x = 3 to x = 4. part

a. find the average rate of change of each section. 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.

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Mathematics

19 July, 06:36

Given the function f (x) = 4 (2) x, section a is from x = 1 to x = 2 and section b is from x = 3 to x = 4. part

a. find the average rate of change of each section. 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.

+4

Answers (1)

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Kiana Stout · Answer 1

A. Average rate of change for x=1 to 2: 4 (2²) - 4 (2) = 16-8=8; from x=3 to 4: 4 (2⁴) - 4 (2³) = 64-32=32.

b. Section b is 32/8=4 times greater. As the exponent of 2 increases, the gaps between consecutive powers of 2 gets wider and therefore the rate of change is greater.