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

- anonymous

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- anonymous

help please @zepdrix

- zepdrix

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

- anonymous

should i take a screenshot better?

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## More answers

- zepdrix

Nah I think we'll be ok :)

- 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.

- 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.

- 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

- zepdrix

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

- anonymous

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

- 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.

- anonymous

Write an exponential function to represent the spread of Ben's social media post.
Write an exponential function to represent the spread of Carter's social media post.
Graph each function using at least 3 points for each line. All graphs should be placed together on the same coordinate plane, so be sure to label each line. You may graph your equation by hand on a piece of paper and scan your work or you may use graphing technology.
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.
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.
How does this graph compare with the original graph of Amber's photo share?
Based on your results, which students' post travels the fastest? How is this shown in the equation form of the functions?
If you had to choose, would you prefer a post with fewer friends initially but more shares, like Amber, or more friends initially but fewer shares? Justify your answer with your calculations from previous questions.

- zepdrix

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

- anonymous

no not really :/

- zepdrix

|dw:1439319322976:dw|

- zepdrix

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

- zepdrix

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

- anonymous

0?

- zepdrix

No. \(\large\rm 4^0\ne0\)

- anonymous

4?

- zepdrix

Anything raised to the 0 power gives us 1.

- anonymous

ok

- zepdrix

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

- zepdrix

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

- anonymous

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

- zepdrix

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

- anonymous

yes my bad i meant a(2)=48

- zepdrix

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

- 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

- anonymous

i know very big :O

- zepdrix

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

- anonymous

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

- zepdrix

|dw:1439320292352:dw|okie good :O

- zepdrix

|dw:1439320398549:dw|

- zepdrix

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

- anonymous

ok

- anonymous

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

- zepdrix

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

- anonymous

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

- anonymous

@zepdrix

- 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.

- zepdrix

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

- anonymous

a=192
b=54
c=80

- zepdrix

mmm k good. and do the same for day 10

- anonymous

a=1048576
b=59049
c=2048

- 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.

- zepdrix

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

- zepdrix

What do you think ?:d

- anonymous

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

- zepdrix

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

- anonymous

does it make all the functions change?

- 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

- zepdrix

bah i gotta go for now :c

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