Question

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

Answer 1

help please @zepdrix

Answer 2

Boy this post is quite a mess :O
I'm not sure what's going on. It's all jumbled up.

Answer 3

should i take a screenshot better?

Answer 4

Nah I think we'll be ok :)

Answer 5

Notice with Amber's function:\[\large\rm A(x)=\color{orangered}{3}(\color{royalblue}{4})^x\]The 3 represents the number of people she initially shared with.
And the 4 will represent the growth rate, ok?
So the amount of people who see her photo each day is increasing by a rate of 4.

Answer 6

Lemme show you how we would construct Ben's function,
and then we'll see if you can come up with one for Carter.

Answer 7

Ben initially shared his photo with \(\large\rm \color{orangered}{2}\) people.
And the amount of people who have seen his photo increases by \(\large\rm \color{royalblue}{3}\) times every day.
So for Ben we would have something like: \(\large\rm B(x)=\color{orangered}{2}(\color{royalblue}{3})^x\)

k? :o

Answer 8

How bout for Carter, what do you think? :d

Answer 9

c(x)=10(2)^x ?

Answer 10

Mmmmm ok good! :)
Those are the 3 functions we wanted to build.
Do we have to do anything with them?
I don't see any questions listed.

Answer 11

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.

Answer 12

Ok so graph, do you understand how to do that?
Remember how to make a t-chart?

Answer 13

no not really :/