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
1 6
2 18 Carter shared his post with 10 friends, who each share with only 2 people each day.

- chrisGA

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- chrisGA

1) 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.
2)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

- chrisGA

can someone help me out or answer this for me i will give medal and fan please and thank you

- ganeshie8

First read the problem and figure out what exactly it is asking to find out

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## More answers

- chrisGA

it asking for how many shares each student's post will have received on Day 3 and then on Day 10

- ganeshie8

Yes, we have 3 students : Amber, Ben, Carter
Amber's shares function is given by
\[f(x) = 3*(4)^x\]
simply plugin \(x=3\) to find the number of shares on day \(3\)

- chrisGA

so that amber share?

- chrisGA

so all you have to do is plugin

- ganeshie8

Right, you do see that function notation is so simple. All you have to do is plug because, when you plugin the day number, "x", the function f(x) spits out the shares on that day.

- chrisGA

yes i see..How about number 2?

- chrisGA

@ganeshie8

- ganeshie8

have you finished with part1 ?

- chrisGA

yes

- chrisGA

Can you help with 2 now

- ganeshie8

could you show me your work for part1

- chrisGA

Amber=f(x)=3∗(4)x
Ben=f(x)=2∗(4)x
Carter=f(x)=10∗(4)x

- ganeshie8

Not quite, Ben's shares are tripling each day, so the function should be
\[f(x) = 2*(3)^x\]
yes ?

- chrisGA

yes

- ganeshie8

your function for Carter also doesnt look correct

- ganeshie8

`Carter shared his post with 10 friends, who each share with only 2 people each day.`
each are sharing with 2 people each day, that means the number of shares are doubling each day, so the function for carter's shares will be
\[f(x) = 10*(2)^x\]

- ganeshie8

plugin x=3, 10 in each of these functions to find the number of shares on 3rd and 10th day

- chrisGA

so it will be f(x)=10∗(2)x??

- ganeshie8

for Carter, it is f(x) = 10*(2)^x

- ganeshie8

Amber=f(x)=3∗(4)^x
Ben=f(x)=2∗(3)x
Carter=f(x)=10∗(2)^x
plugin x=3 and find the number of shares on 3rd day

- chrisGA

ok

- ganeshie8

work it

- ganeshie8

Amber=f(x)=3∗(4)^x
plugin x = 3 :
f(3) = 3*(4)^3 = ?

- chrisGA

so just solve that?

- chrisGA

192?

- ganeshie8

Yes, so on day 3, Amber's photo will be shared to 192 people.

- ganeshie8

similarly find out the number of shares on day 3 for Ben and Carter also

- chrisGA

ok

- chrisGA

ben=52
carter=20

- ganeshie8

doesn't look correct, try again

- chrisGA

for both?

- ganeshie8

Amber=f(x)=3∗(4)^x
Ben=f(x)=2∗(3)x
Carter=f(x)=10∗(2)^x
On 3rd day :
Amber=f(3)=3∗(4)^3 = 192
Ben=f(x)=2∗(3)^3 = ?
Carter=f(x)=10∗(2)^3 = ?

- chrisGA

ben=54
carter=80

- ganeshie8

Looks good! similarly work for day 10 also

- ganeshie8

Amber=f(x)=3∗(4)^x
Ben=f(x)=2∗(3)x
Carter=f(x)=10∗(2)^x
On 3rd day :
Amber=f(3)=3∗(4)^3 = 192
Ben=f(x)=2∗(3)^3 = 54
Carter=f(x)=10∗(2)^3 = 80
On 10th day :
Amber=f(10)=3∗(4)^10 = ?
Ben=f(10)=2∗(3)^10 = ?
Carter=f(10)=10∗(2)^10 = ?

- chrisGA

am i doing the same thing or evaluate?

- ganeshie8

Yes

- chrisGA

samething? or evaluate??

- ganeshie8

ofcourse you need to evaluate to know the shares on 10th day

- chrisGA

carter=10240
ben=118098
Amber=3145728

- ganeshie8

good, so who has more shares on day 10 ?

- ganeshie8

Amber=f(x)=3∗(4)^x
Ben=f(x)=2∗(3)x
Carter=f(x)=10∗(2)^x
On 3rd day :
Amber=f(3)=3∗(4)^3 = 192
Ben=f(x)=2∗(3)^3 = 54
Carter=f(x)=10∗(2)^3 = 80
On 10th day :
Amber=f(10)=3∗(4)^10 = 3145728
Ben=f(10)=2∗(3)^10 = 118098
Carter=f(10)=10∗(2)^10 = 10240

- chrisGA

Amber

- ganeshie8

Yes! why do you think Amber has more shares on day 10 ?
Notice that Amber has started with just 3 shares and Carter started with 10 shares.
Still Carter's shares are very low compared to Amber on day 10. why ?

- chrisGA

becuase as the days went on People started to share amber post more than everyone else

- ganeshie8

Kindof, but a more correct answer would be : Amber's shares are incresing by 4 times each day where as Carter's shares are only increasing by 2 times each day. so Amber's shares are expected to be more on day 10 compared to Carter's

- ganeshie8

we're done with part1

- ganeshie8

for part2, use desmos to graph the 3 functions
https://www.desmos.com/calculator

- chrisGA

i dont know how to use it can you show me the 1st one?

- chrisGA

@ganeshie8

- ganeshie8

do you see a textbox on top right corner ?

- ganeshie8

enter the function there
`f(x)=3∗(4)^x`

- ganeshie8

https://www.desmos.com/calculator/fxnt3ldndm

- ganeshie8

I have plotted the graph of Amber's shares for you above

- chrisGA

https://www.desmos.com/calculator/3t1miijac8

- ganeshie8

Looks perfect!
maybe zoomout the graph a bit if you want... take a screenshot and attach it for part2

- chrisGA

Thank you alot I really appreciate you taking the time to help me understand

- anonymous

f 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?

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