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