Question

PLEASE HELP 99 POINTS

Given the function h(x) = 3(5)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. (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

Presumably, . In that case,

(A)

The average rate of change over the interval is

and over , it's

(B)

, i.e. the average rate of change over the second interval is 25 times higher. That's to be expected; is an exponential function. As gets larger, the rate of change of gets larger too.

Answer 2

Presumably,
`h(x)=3(5)^x`. In that case,

(A)
The average rate of change over the interval
`0\le x\le1` is


`(h(1)-h(0))/(1-0)=\frac{15-3}1=12`

and over
`2\le x\le3`, it's


`(h(3)-h(2))/(3-2)=\frac{375-75}1=300`

(B)

`(300)/(12)=25`, i.e. the average rate of change over the second interval is 25 times higher. That's to be expected;
`3(5)^x` is an exponential function. As
`x` gets larger, the rate of change of
`h(x)` gets larger too.