## anonymous one year ago Three Algebra 1 students are comparing how fast their social media posts have spread. Their results are shown in the following table. Student Amber Ben Carter Description Amber shared her photo with 3 people. They continued to share it, so the number of shares increases every day as shown by the function. Ben shared his post with 2 friends. Each of those friends shares with 3 more every day, so the number of shares triples every day. Carter shared his post with 10 friends, who each share with only 2 people each day. Social Media Post Shares f(x) = 3(4)x Day Number of Shares 0 2

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1. anonymous

2. zepdrix

Boy this post is quite a mess :O I'm not sure what's going on. It's all jumbled up.

3. anonymous

should i take a screenshot better?

4. zepdrix

Nah I think we'll be ok :)

5. zepdrix

Notice with Amber's function:$\large\rm A(x)=\color{orangered}{3}(\color{royalblue}{4})^x$The 3 represents the number of people she initially shared with. And the 4 will represent the growth rate, ok? So the amount of people who see her photo each day is increasing by a rate of 4.

6. zepdrix

Lemme show you how we would construct Ben's function, and then we'll see if you can come up with one for Carter.

7. zepdrix

Ben initially shared his photo with $$\large\rm \color{orangered}{2}$$ people. And the amount of people who have seen his photo increases by $$\large\rm \color{royalblue}{3}$$ times every day. So for Ben we would have something like: $$\large\rm B(x)=\color{orangered}{2}(\color{royalblue}{3})^x$$ k? :o

8. zepdrix

How bout for Carter, what do you think? :d

9. anonymous

c(x)=10(2)^x ?

10. zepdrix

Mmmmm ok good! :) Those are the 3 functions we wanted to build. Do we have to do anything with them? I don't see any questions listed.

11. anonymous

12. zepdrix

Ok so graph, do you understand how to do that? Remember how to make a t-chart?

13. anonymous

no not really :/

14. zepdrix

|dw:1439319322976:dw|

15. zepdrix

For Amber's exponential function, let's try to plot the points for x=0, 1 and 2.

16. zepdrix

So what do you get for A(x)=3(4)^x when you plug x=0 in?

17. anonymous

0?

18. zepdrix

No. $$\large\rm 4^0\ne0$$

19. anonymous

4?

20. zepdrix

Anything raised to the 0 power gives us 1.

21. anonymous

ok

22. zepdrix

$\large\rm A(0)=3(4)^0$$\large\rm A(0)=3(1)$$\large\rm A(0)=3$

23. zepdrix

How bout for x=1 and x=2 what do you get? :O

24. anonymous

a(1)=12 a(2)=16

25. zepdrix

a(2) = 3*16 ya? i think you forgot the 3

26. anonymous

yes my bad i meant a(2)=48

27. zepdrix

|dw:1439319841779:dw|Ok good. Do you understand how I used that information to plot the three locations?

28. zepdrix

You can do your axes a little differently if you want. I dunno how you're going to be able to fit the points for all three functions on one graph :P it's going to look so ugly

29. anonymous

i know very big :O

30. zepdrix

|dw:1439320055865:dw|How bout for Ben. What values are we going to get?

31. anonymous

b(0)=2 b(1)=6 b(2)=18

32. zepdrix

|dw:1439320292352:dw|okie good :O

33. zepdrix

|dw:1439320398549:dw|

34. zepdrix

See if you can figure out the values for C. I brb

35. anonymous

ok

36. anonymous

c(0)=10 c(1)=20 c(2)=40

37. zepdrix

sorry i had to go take care of some stuff :O you get this one finished?

38. anonymous

its ok and no i still have 4-7 do to :(

39. anonymous

@zepdrix

40. zepdrix

Using the functions for each student, predict how many shares each student's post will have received on Day 3 and then on Day 10. Justify your answers.

41. zepdrix

The x corresponds to the day. So for day 3, you're simply calculating: $$\large\rm A(3)=?$$ $$\large\rm B(3)=?$$ $$\large\rm C(3)=?$$

42. anonymous

a=192 b=54 c=80

43. zepdrix

mmm k good. and do the same for day 10

44. anonymous

a=1048576 b=59049 c=2048

45. zepdrix

Ya that's prolly right :d Ok next part saysssss If Amber decides to mail copies of her photo to the 45 residents of her grandmother's assisted living facility, the new function representing her photo shares is f(x) = 3(4)x + 45.

46. zepdrix

How does this graph compare with the original graph of Amber's photo share?

47. zepdrix

What do you think ?:d

48. anonymous

it is basically the same thing you just have to add 45 to the equation

49. zepdrix

but what does adding 45 to the equation... do to the picture?

50. anonymous

does it make all the functions change?

51. zepdrix

what? 0_o no, only amy's. or ashley... amber. whatever. Aight, you not getting it :d this is the word they're looking for: vertical shift. Adding 45 to the function will shift the line up by 45

52. zepdrix

bah i gotta go for now :c