07.02 Analyzing Exponential Functions Project How much do you share on social media? Do you have accounts linked to your computer, phone, and tablet? The average teen spends around 9 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 2 student scenarios to see how social media spreads. Four student scenarios are described in the table below. Work together with your partner to decide on who will study which two students.

Student Harrison Anita Juan Krista
Description Harrison shared his video with 7 friends. His friends continued to share it, doubling the number of viewers each day. Anita shared her photo with 41 followers. Each of them shared it with 2 friends, doubling the number of viewers each day. Juan shared his post with 4 friends, who each shared it with 4 more friends. They continued sharing at the same rate. Krista shared her photo with 6 friends, who each shared it with 3 friends. This pattern continued.
Social Media Shares f(x) = 7(2)x
Day
0
1
2
Viewers
41
82
164 Juan shared his post with 4 friends, who each shared it with 4 more friends. They continued sharing at the same rate. f(x) = 6(3)x
State which two students you are studying so your instructor knows for whom each partner is responsible.
Provide an exponential function representing Anita's social media shares.
Provide an exponential function representing Juan's social media shares.
Using the functions for each student, predict how many shares each student's post will have received on Day 3 and then on Day 10. Justify your answers.
Based on your results, which student's 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 or more friends initially but fewer shares? Does your partner agree or disagree? Can you think of reasons why more or fewer shares are preferable? Justify your answer with your calculations from previous questions.