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 1

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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 1

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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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.
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 3 points for each line. All graphs should be placed together on the same coordinate plane, so be sure to label each line. 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 have 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 students' 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 questions.
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