Question

Given the function f(x) = 5x, 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

@TheSmartOne @jim_thompson5910

Answer 2

Would A be 7.5?

Answer 3

@.Sam. @sammixboo @agent0smith

Answer 4

how are you getting 7.5?

Answer 5

0 times 5 is 0 and 1 times 5 is 5. 2.5. 2 times 5 is 10 and 3 times 5 is 15. So uh 5 then..?

Answer 6

f(x) = 5x
f(0) = 5*0
f(0) = 0


f(x) = 5x
f(1) = 5*1
f(1) = 5


So we have the two points (0,0) and (1,5)

Answer 7

find the slope through (0,0) and (1,5) to find the average rate of change for section A

Answer 8

slope is 5. Rate of change is 5?

Answer 9

yes

Answer 10

what about the slope of section B?

Answer 11

wait, is the function f(x) = 5x
OR
is it f(x) = 5^x
??

Answer 12

(2, 10) (3, 15) so 5?

Answer 13

5^x

Answer 14

ok be careful about inserting exponents

Answer 15

redo section A and B again with this new function

Answer 16

(0, 5) (1, 25) ?

Answer 17

section B is from x = 2 to x = 3

Answer 18

Is section a correct?

Answer 19

yes

Answer 20

Wait what does 5^1 =?

Answer 21

actually, no, sorry

Answer 22

f(x) = 5^x
f(0) = 5^0
f(0) = 1

Answer 23

5^0 is not 0

Answer 24

Its 5.

Answer 25

oh nvm..

Answer 26

(0, 1) and (1, 5) for a?

Answer 27

as stated earlier, if you plug in x = 0 into f(x) = 5^x, you get 1 as a result

Answer 28

oh nvm I see what you mean now

Answer 29

yes section A is from (0,1) to (1,5). Compute the slope of this

Answer 30

4.

Answer 31

yes

Answer 32

how about section B?

Answer 33

(2, 25) (3, 625) 600 is slope for that

Answer 34

5^3 isn't 625

Answer 35

oh oops
125, so slope is 100

Answer 36

yes

Answer 37

`How many times greater is the average rate of change of Section B than Section A?`

fill in the blank

B = _______*A

where B refers to "slope of section B" and A refers to "slope of section A"

Answer 38

A: For section A its 4, and section B its 100.

B: 25 times. Its much bigger because x = 2 and x = 3 are bigger than x = 0 and x = 1.

Answer 39

Is that correct?

Answer 40

I agree with the first part of your answer in part B, but you should be more specific in the second part of part B

Answer 41

`Its much bigger because x = 2 and x = 3 are bigger than x = 0 and x = 1.`
is too vague in my opinion

Answer 42

Is that fine for an assignment when you are 13? XD

Answer 43

I guess it depends on your teacher, but I'd include the term "exponential function" in there somewhere

Answer 44

I dont know what that means.

Answer 45

Exponential growth functions have a property that the average rate of change increases over time