Question

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)

Answer 1

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