How much do you share on social media? Do you have accounts linked to your computer, phone, and tablet? The average teen spends around 5 hours per day online, and checks his or her social media account about 10 times each day. When an image or post is shared publicly, some students are surprised at how quickly their information travels across the Internet. The scary part is that nothing online is really private. All it takes is one friend sharing your photo or updates with the public to create a very public viral trend.

For this project, you will use what you have learned about exponential functions to study what happens if a social media post is shared publicly.

Social Sharing
You and your partner will each study two student scenarios to see how social media spreads. Four student scenarios are described in the table below. Work together with your partner to decide who will study which two students:

Student Henry Isabelle Javier Kendra
Description Henry shared his video with 4 friends. His friends continued to share it, doubling the number of viewers each day. Isabelle shared her photo with 51 followers. Each of them shared it with 2 friends, doubling the number of viewers each day. Javier shared his post with 4 friends, who each shared it with 4 more friends. They continued sharing at the same rate. Kendra shared her photo with 11 friends, who each shared it with 3 friends. This pattern continued.
Social Media Shares f(x) = 4(2)x
Day Viewers
0 51
1 102
2 204 Javier shared his post with 4 friends, who each shared it with 4 more friends. They continued sharing at the same rate. f(x) = 11(3)x

Question: Graph the exponential functions for all four students. If possible, place them all on 1 graph. If not, be sure to work with your partner so you have access to all graphs. 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.