Question

100! POINTS

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 together with your partner to decide on who will study which two students

1. State which two students you are studying so your instructor knows for whom each partner is responsible 2.Provide an exponential function representing Anita's social media shares 3. Provide an exponential function representing Juan's social media shares 4.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 answer 5.Based on your resultswhich student's post travels the fastest? How is this shown in the equation form of the functions? 6. 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 fewer shares are preferable? Justify your answer with your calculations from previous questions

Answer 1

General form of an exponential function:
`y=ab^x`

where:

• a is the initial value
• b is the growth factor
• x is the independent variable
• y is the dependent variable

Anita's initial value is 41 and the number of viewers doubles each day

`\implies f(x)=41(2)^x`

Juan's initial value is 4 and the number of views quadruples each day

`\implies f(x)=4(4)^x`

Day 3

`\textsf{Harrison}:f(3)=7(2)^3=56`

`\textsf{Anita}:f(3)=41(2)^3=328`

`\textsf{Juan}:f(3)=4(4)^3=256`

`\textsf{Krista}:f(3)=6(3)^3=162`

Day 10

`\textsf{Harrison}:f(10)=7(2)^(10)=7168`

`\textsf{Anita}:f(10)=41(2)^(10)=41984`

`\textsf{Juan}:f(10)=4(4)^(10)=4194304`

`\textsf{Krista}:f(10)=6(3)^(10)=354294`

Juan's post travels the fastest.

This is shown by the growth factor in the equation form of the functions.

Juan's equation has the largest growth factor of 4.