Given the function h(x) = 4x, 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)

The average rate of change is the sloope from the points at the end

find slope from (0,h(0)) to (1,h(1)) for section A and from (2,h(2)) to (3,h(3)) for section B

h(0)=0
h(1)=4
h(2)=8
h(3)=12

slope between (x1,y1) and (x2,y2) is (y2-y1)/(x2-x1)

so

A.

section A is from (0,0) to (1,4)
slope=(4-0)/(1-0)=4/1=4

section B is from (2,8) to (3,12)
slope=(12-8)/(3-2)=4/1=4

B.
they are the same
what

maybe you meant h(x)=4ˣ

in that case
h(0)=1
h(1)=4
h(2)=16
h(3)=64

then

A.
section A is from (0,1) to (1,4)
slope is (4-1)/(1-0)=3/1=3

section B is from (2,16) to (3,64)
slope is (64-16)/(3-2)=48/1=48

B.
how many times
3 times what=48
divide both sides by 3
what=16
16 times greater
it is greater because it's an exponential function