Question

Work Independently
How much do you share on social media? Do you have accounts linked to your computer, phone, and tablet? The average teen spends around five hours per day online, and checks his or her social media account about 10 times each day.

When an image or post is shared publicly, some students are surprised at how quickly their information travels across the Internet. The scary part is that nothing online is really private. All it takes is one friend sharing your photo or updates with the public to create a very public viral trend.

For this project, you will use what you have learned about exponential functions to study what happens if a social media post is shared publicly.

Social Sharing
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 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 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

Answer 1

This table, can you upload it so that it doesn't look skewed, attach file button down below

Answer 2

Here is the full file

Answer 3

I will do whatever you want if you help me

Answer 4

bruh no need for that, im in school rn and your problem looks pretty long, so how about i help u in a few hours. sound good?

Answer 5

ok

Answer 6

Alright, lets break this down.
Lets start with number 1 and 2.
So for 1, we need to represent an exponential function to describe Ben's social media post growth.

Quick q, is this algebra 2 or precalc, so i know how to explain to u

Answer 7

Algebra 2

Answer 8

Okay so We are given some points, (0,2) (1,6) (2,18)
Now we are going to use the equations of
\[y = a \times b^x\]
Where we plug in y and x-values respectively

Answer 9

Now we can plug in values to find what a and b are.
So
\[2 = a \times b^0\] and
\[6 =a \times b^1\]

Answer 10

We can then evaluate b^0 as 1, so that means that
\[2 = a \times 1\]
or that a =2,
Now solving for b,
We know that a is 2 so we plug into the other equation
\[6 = a \times b^1\]
b^1 = b
\[6 = 2 \times b\]
And hence we get b =3

So our final exponential equation for Ben is
\[y = 2 \times 3^x\]
And you can test this out by plugging in 2 and seeing if you get 18. :)

Answer 11

We are done with part 1, on to part 2.
So we just need to decipher the word problem into an equation.
He originally shares with 10 friends, so that is the coefficient, or a
Now they share with 2 people every day, so we will have a base (b) = 2
So then our equation for Carter is
\[y = 10 \times 2^x\]

Answer 12

Now you just have to graph the functions by hand (use the rules, plot known points, and fit a smooth curve through them) or use desmos for Part 3

Answer 13

Then for part 4 you need to predict how many shares each student receives on day 3 and on day 10, so for each of the equations we derived above, just plug in 3 and 10 for the x to find the shares that those students received on days 3 and 10 respectively.
So for example Amber's equation is \[3(4)^x\]
plug in 3 for x we get
\[3(4)^3 = 192\]
So that means on day 3 amber gets 192 shares, you want to do that for days 3 and 10 for each of the 3 people. I just did one for you as a starter

Answer 14

Then for part 5, we see Amber's new function, which is a translation of her original function by 45 units (shares in this case) up, you probably want to go into a bit more detail by comparing the 2 graphs of Amber, I would recommend plotting them to help analyze

Answer 15

Now based on your equations, for part 6, it is based on the base of the function. For example if you graph the 3 functions of the students, the graph that goes to infinity first would be the one who's post travels the fastest. For example if we consider these 2 graphs right her
We can graphically see that the black function will travel farther then the red one because it goes to infinity faster

Answer 16

Another way to mathematically represent which student's post travels the fastest, you can just look at the base. If we take a look, Amber has a base of 4, Ben has a base of 3, and carter has a base of 2. Now carter has the largest coefficient (10) so he would initially have the most amount of shares for the first few days, but since he has a smaller base, he would not gain as many shares as the other 2 and that means that his wouldn't travel the fastest. (he would initially have the most shares out of the 3 for the first few days but then the others will cross him). Now Ben has a small coefficient 2 and a small base of 3, compared to Amber who has a coefficient of 3 with a base of 4. Now that means that Ben never will have more shares then Amber. Amber's would travel the fastest because he has the biggest base.

Answer 17

Now for the last question that is entirely on you boy/girl. You choose which you would want. If you have any questions you can ask. Ik that I threw a lot at you but I wouldn't type it if it isn't helpful. Have a great day :) Also be sure to click best response, I appreciate it.

Answer 18

ok