Three Algebra 1 students are comparing how fast their social media posts have spread. Their results are shown in the following table; Student
Description

Amber shared her photo with 3 people. They continued to share it, so the number of shares increases everyday, as shown. f(x) = 3(4)^x.

Ben shared his post with 2 friends. Each of those friends shared with 3 more everyday, so the number of shares triples every day.
f(x) 3(4)
Day0, 2 (number of shares)
Day1, 6 (number of shares)
Day2, 18 (number of shares)

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

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

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

3. 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.

4. Using the functions for each student, predict how many shares each students post will be recieved on day 3 and then on day 10. Justify your answers.

5. If amber decides to mail copies of her photo to the 45 residents of her grandmothers assisted living facility, the new function representing her photos shares is f(x) = 3(4)^x + 45. How does this graph compare with the original graph of ambers photo share?

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