Question

Given the function f(x) = 2(3)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.

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.

Answer 1

f(0) = 2(3)(0) = 0 ⇒ (0, 0)

f(1) = 2(3)(1) = 6 ⇒ (1, 6)

rate of change from x = 0 to x = 1

`(y2 - y1)/(x2 - x1)` =
`(6 - 0)/(1 - 0)` =
`(6)/(1)` = 6

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f(2) = 2(3)(2) = 12 ⇒ (2, 12)

f(3) = 2(3)(3) = 18 ⇒ (3, 18)

rate of change from x = 2 to x = 3

`(y2 - y1)/(x2 - x1)` =
`(18 - 12)/(3 - 2)` =
`(6)/(1)` = 6

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Since it is the same line, they will have the same slope (aka rate of change).