Help! 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,
Social
Media Post
Shares
f(x) = 3(4)
Ben shared his post with 2 friends. Each of those friends Carter shared his post with 10
shares with 3 more every day, so the number of shares friends, who each share with only 2
triples every day.
people each day
Day Number of Shares
Carter shared his post with 10
friends, who each share with only 2
0
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 student's post will be received 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 grandmother's assisted living facility, the new function representing her photo shares is f(x) =
3(4)* + 45. How does this graph compare with the original graph of Amber's photo share?
6. Based on your results, which students' post travels the fastest? How is this shown in the equation form of the functions?
7. 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.