Question

I AM GIVING 45 POINTS IF YOU DO THE WHOLE HOMEWORK CORRECTLY!!!!!!!!!!!!!

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

Student: Amber / Ben / Carter
Description: Amber shared her photo with 3 people. They continued to share it, so the number of shares increases every day, as shown by the function. / Ben shared his post with 2 friends. Each of those friends shares with 3 more every day, so the number of shares triples every day. / Carter shared his post with 10 friends, who each share with only 2 people each day.
Social Media Post Shares: f(x) = 3(4)x
Day: Number of Shares:
0 2
1 6
2 18
Carter shared his post with 10 friends, who each share with only 2 people each day.

1. Write an exponential function to represent the spread of Ben's social media post.
2. Write an exponential function to represent the spread of Carter's social media post.
3. 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.
4. 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.
5. 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?
6. Based on your results, which student's post travels the fastest? How is this shown in the equation form of the functions?
7. 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.

Answer 1

1. The exponential function to represent the spread of Ben's social media post is f(x) = 2(3)^x

2. The exponential function to represent the spread of Carter's social media post is f(x) = 10(2)^x

4. To predict how many shares each student's post will be received on Day 3 and Day 10, substitute the respective values of x into each function:

a) On Day 3, Amber's post will have f(3) = 3(4)^3 = 192 shares. On Day 10, Amber's post will have f(10) = 3(4)^10 = 6,291,456 shares.

b) On Day 3, Ben's post will have f(3) = 2(3)^3 = 54 shares. On Day 10, Ben's post will have f(10) = 2(3)^10 = 196,830 shares.

c) On Day 3, Carter's post will have f(3) = 10(2)^3 = 80 shares. On Day 10, Carter's post will have f(10) = 10(2)^10 = 10240 shares.

5. The graph of Amber's post with copies mailed to the assisted living facility will have the same shape and growth rate as the original function, but it will be shifted upwards by 45 units along the y-axis.

6. Ben's post travels the fastest because it has the largest growth rate of 3 (compared to Amber's 4 and Carter's 2), meaning it triples every day.

7. It depends on the specific purpose of the post. If the goal is to have a widespread influence and viral impact, then Amber's approach of starting with a smaller group of initial shares but a higher growth rate might be more effective. On the other hand, if the goal is to create a more tight-knit network of shares with a smaller number of initial friends, then Carter's approach might be more appropriate.