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.
Write an exponential function to represent the spread of Ben's social media post.
Write an exponential function to represent the spread of Carter's social media post.
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.
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.
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?
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, like Amber, or more friends initially but fewer shares? Justify your answer with your calculations from previous question
do this in one paragraph with the vocabulary of a 5th grader
Ben's social media post can be represented by the exponential function f(x) = 2(3)^x. This means that the number of shares on each day triples.
Carter's social media post can be represented by the exponential function f(x) = 10(2)^x. In this case, each friend shares with only 2 people each day.
To predict the number of shares on Day 3, we can plug in x = 3 into the functions. For Ben's post, f(3) = 2(3)^3 = 2(27) = 54 shares. For Carter's post, f(3) = 10(2)^3 = 10(8) = 80 shares.
To predict the number of shares on Day 10, we can plug in x = 10 into the functions. For Ben's post, f(10) = 2(3)^10 = 2(59049) = 118,098 shares. For Carter's post, f(10) = 10(2)^10 = 10(1024) = 10,240 shares.
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 would be f(x) = 3(4)^x + 45. This new function would have a constant addition of 45 shares, so the graph would be shifted upward by 45 units compared to the original graph of Amber's photo share.
Based on the results, Carter's post travels faster as it reaches a higher number of shares compared to Amber's and Ben's posts. This is shown in the exponential equation f(x) = 10(2)^x, where the base 2 represents the multiplying factor for each day.
If I had to choose, I would prefer a post with more friends initially but fewer shares. This is because with more friends initially, the potential reach of the post is wider. Even though there are fewer shares per day, the cumulative effect of having more friends can result in a higher number of shares over time.
do all of that in 6 sentences
Ben's social media post can be represented by the exponential function f(x) = 2(3)^x, where the number of shares triples each day. Carter's post can be represented by the function f(x) = 10(2)^x, with each friend sharing with only 2 people each day. On Day 3, Ben's post is predicted to have 54 shares, while Carter's post is predicted to have 80 shares. On Day 10, Ben's post is predicted to have 118,098 shares, while Carter's post is predicted to have 10,240 shares. If Amber mails copies of her post to the 45 residents of her grandmother's assisted living facility, her new function is f(x) = 3(4)^x + 45, and the graph would shift upward by 45 units. Carter's post is faster as it reaches a higher number of shares, shown in the equation form, and I would prefer a post with more friends initially but fewer shares to have a wider reach over time.
To represent the spread of Ben's social media post, we can use the exponential function f(x) = 2(3)^x because each friend he shares with triples the number of shares every day. For Carter's social media post, we can use the exponential function f(x) = 10(2)^x because each of his friends only shares with 2 people each day.
To graph these functions, we can choose three points for each curve. For Ben's post, the points could be (0, 2), (1, 6), and (2, 18). For Carter's post, the points could be (0, 10), (1, 20), and (2, 40). We can plot these points on a coordinate plane.
To predict the number of shares on Day 3, we can substitute x = 3 into the respective functions. For Ben, f(3) = 2(3)^3 = 2(27) = 54 shares. For Carter, f(3) = 10(2)^3 = 10(8) = 80 shares. On Day 10, for Ben, f(10) = 2(3)^10 = 2(59049) = 118098 shares. For Carter, f(10) = 10(2)^10 = 10(1024) = 10240 shares.
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. This graph will be similar to the original graph of Amber's photo share, but it will be shifted upward by 45 units because of the additional shares she mailed.
Based on the results, Carter's post travels the fastest because his number of shares increases rapidly. This is shown in the equation form of the functions, where the base number (3 for Ben and 2 for Carter) is greater than the base number for Amber's post (4).
I would prefer a post with fewer friends initially but more shares, like Amber's. This is because her post grows steadily and with the additional shares she mailed, it can reach a larger audience. Carter's post may spread faster initially, but it may not reach as many people in the long run.