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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)

User Zlidime
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2 Answers

5 votes

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.

User Ambat Bhath
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7.9k points
3 votes
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.
User Espinosa
by
8.0k points

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