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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.

Answer :

scme1702
A)
f(2) - f(1) = 4(2)² - 4(2)
= 8
f(4) - f(3) = 4(2)⁴ - 4(2)³
= 32

B)
32/8 = 4
The rate of change is 4 times more in section B than in A.

The large difference is due to the fact that this is an exponential function and each unit step is larger than the last.

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