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.

- anonymous

- katieb

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- Excalibur0126

What's the question?

- anonymous

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

##### 1 Attachment

- Nnesha

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

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## More answers

- anonymous

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

- Nnesha

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)= ??

- Nnesha

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

- anonymous

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

- Nnesha

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

- Nnesha

\[\huge\rm f(0)=5^0 ~~~~~~f(1)=5^1\]
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

- Nnesha

does it make sence ?

- Nnesha

sense *

- anonymous

I have no idea whats hapenning @Nnesha

- Nnesha

5^0 = ?

- Nnesha

5 to the zero power equal to what ?

- anonymous

5?

- Nnesha

no did you read my comments ^^??

- anonymous

*1 (im kind of slow with math)

- Nnesha

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

- anonymous

thats y2 - y1 over x2 - x1?

- Nnesha

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

- anonymous

5-1 over 1-0?

- anonymous

4 over 1 is the slope?

- Nnesha

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

- Nnesha

now find y when x=2 and x=3

- Nnesha

section B^

- anonymous

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

- Nnesha

great now find slope!

- anonymous

100 over 1?

- Nnesha

nice now you can write answer for PART B

- anonymous

Wait what was the answer for part A?

- Nnesha

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

- anonymous

Its just the two slopes?

- Nnesha

yes right!

- anonymous

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

- Nnesha

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

- anonymous

so i write 4 and 100?

- Nnesha

ye

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