Answer:
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.
Social Media Post Shares
f(x) = 3(4)x F(X)=2(3) ^x F(x)=10(2) ^x
Write equations for each post (fill in the blanks)
Student Amber Ben Carter
Initial Post 3 2 10
Rate of Growth 300% or 3.0 200% or 2.0 1000% or 10.0
Equation f(x) = 3(1.00 + 3.00)x
f(x) = 3(4)x f(x) =2(1.00+3.00)
f(x) =2(4) x f(x) = 10(1.00+2.00)
f(x) =10(3) x
Using the information from the table above answer the following (use the ^ symbol for exponents):
1. Write an exponential function to represent the spread of Ben’s social media post.
F(x)= 2(4) x
This line will be labeled g(x).
2. Write an exponential function to represent the spread of Carter’s social media post.
F(x)= 10(3) x
This line will be labeled h(x).
3. 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.
4. You may graph your equation by hand on a piece of paper and scan your work or
5. you may use graphing technology.
Paste your graph below:
Notes: The side containing the numbers 1 through 8 is labeled Days the number of shared people grew. And the x axis (the side containing the 1-15) is the side that is labeled Friends shared with.
4. Using the functions for each student, predict how many shares each student’s post will have received on Day 3 and Day 10. Justify your answers.
Day = x Amber Ben Carter
3
3 x
Since the number of people shared with is unknown, we must multiply the number of days (x) by the number of people initially shared with. 54 shares
We know that Ben initially shared his post with 2 friends whom of which then decided to share it with 3 of their friends per day so I would take the last number that we have in the table and multiply it by 3. 80 shares
Carter initially shared his post with 10 friends who later shared it with 2 friends per day. So I made a table that looked like this:
0 10
1 20
2 40
3 80
The pattern is times 2 per day, so you must take the last number in the table from the row before that and multiply it by 2 to get your answer
10 10 x
Since the number of people shared with is unknown, we must multiply the number of days (x) by the number of people initially shared with. There would be 118,098 shares. We know that after 3 days there would be 54 shares, so I took that number and multiplied it by 3, I did this seven times since 3+7=10. And the number that we were looking for WAS 10. There would be 10,240 shares. We know that after 3 days there would be 80 shares so I took 80 and multiplied it by 2 then took that number and did the same, I did this 7 more times since 7+3=10 and the number that we were looking for WAS 10.
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?
This graph would move UP by 45 since you are adding 45 to the initial function.
6. Based on your results, which students’ post travels the fastest? How is this shown in the equation form of the functions?
The student who has the fastest traveling post is Ben. This is shown by the table:
0 2
1 6
2 18
3 54
4 162
5 486
6 1458
7 4374
8 13122
9 39366
10 118098
Ben chose to share his post with only 2 friends but a little went a long way
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.
I would do my share like Ben and ONLY share it with 2 friends and let them share with however many they want. This would mean that I would choose to share it with initially FEW friends and have a lot of shares. I mean look at the table Bens share went a LONG way. I cant paste the table but it is up top.
