## anonymous one year ago 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.

1. Excalibur0126

What's the question?

2. anonymous

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

3. 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

4. anonymous

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

5. 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)= ??

6. Nnesha

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

7. anonymous

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

8. 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

9. 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

10. Nnesha

does it make sence ?

11. Nnesha

sense *

12. anonymous

I have no idea whats hapenning @Nnesha

13. Nnesha

5^0 = ?

14. Nnesha

5 to the zero power equal to what ?

15. anonymous

5?

16. Nnesha

17. anonymous

*1 (im kind of slow with math)

18. 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

19. anonymous

thats y2 - y1 over x2 - x1?

20. Nnesha

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

21. anonymous

5-1 over 1-0?

22. anonymous

4 over 1 is the slope?

23. Nnesha

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

24. Nnesha

now find y when x=2 and x=3

25. Nnesha

section B^

26. anonymous

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

27. Nnesha

great now find slope!

28. anonymous

100 over 1?

29. Nnesha

nice now you can write answer for PART B

30. anonymous

Wait what was the answer for part A?

31. Nnesha

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

32. anonymous

Its just the two slopes?

33. Nnesha

yes right!

34. anonymous

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

35. Nnesha

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

36. anonymous

so i write 4 and 100?

37. Nnesha

ye