Question

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 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.