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
1 6
2 18 carter shared his post with 10 friends, who each share with only 2 people each day.
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 three points for each curve. all graphs should be placed together on the same coordinate plane, so be sure to label each curve. 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 be 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.

an exponential function has the following form:

f(x) = a(b)^x

where a is the initial value, and b is the rate of growth or decay.

Write an exponential function to represent the spread of Ben's social media post.

Ben shared his post with 2 friends, so that is the initial value. Since the number of shares triples every day, this is the rate of growth.

so the exponential function for Ben will be

f(x) = 2(3)^x

Write an exponential function to represent the spread of Carter's social media post.

Carter shared his post with 10 friends, so that is the initial value. Each friend share with only 2 people each day, so this is the rate of growth.

so the exponential function for Carter will be

f(x) = 10(2)^x

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

For Amber the function is f(x) = 3(4)^x

after 3 days

f(3) = 3(4)^3

f(3) = 3*64

f(3) = 192

after 10 days

f(10) = 3(4)^10

f(10) = 3*1,048,576

f(10) = 3,145,728

For Ben the function is f(x) = 2(3)^x

after 3 days

f(3) = 2(3)^3

f(3) = 2*27

f(3) = 54

after 10 days

f(10) = 2(3)^10

f(10) = 2*59,049

f(10) = 118,098

For Carter the function is f(x) = 10(2)^x

after 3 days

f(3) = 10(2)^3

f(3) = 10*8

f(3) = 80

after 10 days

f(10) = 10(2)^10

f(10) = 10*1,024

f(10) = 10,240

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

the graph is translated 45 units up

Based on your results, which students' post travels the fastest? How is this shown in the equation form of the functions?

Amber's post travels faster because it has the greater rate of growth. This is shown on the b value of the equation.

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?  

It is better to have more shares, because at the beginning  you'll have less views, but with more shares it will quickly raise and suppras the ones with more initial views but less shares.  

step-by-step explanation:

the shape,the size and the distance