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
State which two students you are studying so your instructor knows for whom each partner is responsible.
Provide an exponential function representing Isabelle's social media shares.
Provide an exponential function representing Javier's social media shares.
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.
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.
Based on your results, which students' post travels the fastest? How is this shown in the equation form of the functions?
If Henry decides to mail copies of his video to the 45 residents of his grandmother's assisted living facility, the new function representing his video is f(x) = 4(2)x + 45. How does this graph compare with the original graph of Henry's video share?
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.