Question

Given the function \(f(x) = 5^x\), Section A goes from \(x = 0\) to \(x = 1\). Section B goes from \(x = 2\) to \(x = 3\).

Part A: Find the average rate of change for each section.

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.

Answer 1

What's the question?

Answer 2

I'm not too sure how to do this @Excalibur0126

Answer 3

formula to find average rate of change (slope ) \[\huge\rm \frac{ y_2 -y_1 }{ x_2 -x_1 }\]
given: x = 0 and x=1
substitute x for 0 and for 1 into \[\rm f(x)=5^x\]to find y


`f(x) is same as y

Answer 4

0 is x^1? what is x^2 and y^2? @Nnesha

Answer 5

it's not x^2 (not squared)
\[\huge\rm y_2\] means 2nd y
you need two order pairs to find slope
(x , y)(x,y)
(0 , ?) ( 1,y)
you should find y value when x = 0
so replace x with 0 \[\huge\rm f(0)=5^{0}\] f(0)= ??

Answer 6

exponent rule anything to the zero power is one \[\rm (anything)^0 = 1 ~~~(x)^0=1
\]

Answer 7

So what are the steps to doing something like this in the simplest terms? @Nnesha

Answer 8

well
first step) find y when x=0 , x=1
2nd step) find y when x=2 and x=3
when you get all y values then you can apply slope formula to find average rate of change

Answer 9

\[\huge\rm f(0)=5^0 ~~~~~~f(1)=5^1\]
like i said f(x) is same as y so you replace f(0) and f(1) with y \[\large\rm y=5^0 ~~~~~~~~~~y=5^1\]
simplify that^^
(0 , ?)( 1,?)
when x=0 , y = ??
when x=1 y =what ?
write your answer where i put the question marks

Answer 10

does it make sence ?

Answer 11

sense *

Answer 12

I have no idea whats hapenning @Nnesha

Answer 13

5^0 = ?

Answer 14

5 to the zero power equal to what ?

Answer 15

5?

Answer 16

no did you read my comments ^^??

Answer 17

*1 (im kind of slow with math)

Answer 18

yes right
so when x=0 y = 1
(0 ,1) now replace x with 1
\[y=5^1\]
5^1 is same as 5 right
so when x =1 y=5
(0 , 1)(1,5) two order pairs now you can use slope formula to find average rate of change

Answer 19

thats y2 - y1 over x2 - x1?

Answer 20

yes right use these two points (0,1)(1,5)

Answer 21

5-1 over 1-0?

Answer 22

4 over 1 is the slope?

Answer 23

perfect! that's average rate of change when x=0 and x=1 now

Answer 24

now find y when x=2 and x=3

Answer 25

section B^

Answer 26

(x=2 y=25)
(x=3 y=125)

Answer 27

great now find slope!

Answer 28

100 over 1?

Answer 29

nice now you can write answer for PART B

Answer 30

Wait what was the answer for part A?

Answer 31

find average rate of change of `each` section
average rate of change = `slope` we just found the answer

Answer 32

Its just the two slopes?

Answer 33

yes right!

Answer 34

oh okay so For A should I write 4 over 1 and 100 over 1?

Answer 35

2/1 is same as 2
so 4/1 is same as 4

Answer 36

so i write 4 and 100?

Answer 37

ye