Question

I NEED HELP ASAP! WILL NAME YOU BRAINIEST!

Answer 1

Answer:

Write an exponential function to represent the spread of Ben's social media post:

Ben's function is f(x)=2(3)x

Write an exponential function to represent the spread of Carter's social media post:

Carter's function is f(x)=10(2)x

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.

(I have it attached below. Also, I was not able to label each curve on the graph, so on the bottom, each name has it's own color so that you can refer to it when looking for it in the graph.)

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.

Amber will have 192 shares on day 3. Ben will have 54 shares on day 3. Carter will have 80 shares on day 3. Amber will have 3,145,728 shares on day 10. Ben will have 118,098 shares on day 10. Carter will have 10,240 shares on day 10. 

y=3(4)^3 = 3 x 64= 192 - Amber

y=3(4)^10=3 x 1,048,576= 3,145,728-Amber

y=2(3)^3 = 2 x 27=54-Ben

y=2(3)^10= 2 x 29,049=118,098-Ben

y=10(2)^3 = 10 x 8= 80- Carter

y=10(2)^3=10 x 1,024=10,240-Carter

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?

Both graphs would be exponential growth, though the new one goes up by 45 units from the original graph. 

Based on your results, which students' post travels the fastest? How is this shown in the equation form of the functions?

Amber's post travels the fastest because by day 10, she has more than 25 times the shares of her closest competitor. Additionally, her growth factor is 4, while Bens is 3 and Carter is 2.

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 prefer a post with fewer friends but initially more shares, like amber, because my post will spread faster. We can see that even though Amber had only a few friends, her shares grew from 192 shares from day 3 to  3,145,728 on day 10.

Remember the graph is down below, so do not forget! I hope this helps! Have a great day!

Answer 2

Answer:

1. y = 2(3)ˣ; 2. y = 10(4)^x

4. Amber = 192 and 3 145 728; Ben has 54 and 11 098; Carter = 80 and 10 249 shares;

5. Shifted up 45 shares; 6. Amber's; 7. Fewer friends. more shares.

Step-by-step explanation:

The general equation for an exponential function is

y = a(b)ˣ

1. Ben's function

The initial value a = 2.

6 = 2(b)¹ = 2b

b = 3

Ben's function is  

y = 2(3)^x

2. Carter's function

Carter shared his post with 10 friends on Day 0, so  a= 10.  

Each friend shared with 2 people each day, so b = 2.

Therefore, Carter's function is

y=10(2)ˣ

3. Graphs

$\begin{array}{cccc}& \textbf{Amber} &\textbf{Ben} & \textbf{Carter}\\\mathbf{x} & \mathbf{3(4)^{x}} &\mathbf{2(3)^{x}} & \mathbf{10(2)^{x}}\\0 & 3 & 2 & 10\\1 & 12 & 6 & 20\\2 & 48 & 18 & 40\\3 & 192 & 54 & 80\\\end{array}$

The figure below shows the graphs for each function.

4. Predictions

(a) Amber

(i) Day 3

y = 3(4)³  = 3 × 64 = 192

(ii) Day 10

y = 3(4)¹⁰  = 3 × 1 048 576 = 3 145 728

(b) Ben

(i) Day 3

y = 2(3)³  = 2 × 27 = 54

(ii) Day 10

y = 2(3)¹⁰  = 2 × 29 049 = 118 098

(c) Carter

(i) Day 3

y = 10(2)³  = 10 × 8 = 80

(ii) Day 10

y =10(2)¹⁰  = 10 × 1024 = 10 240

5. Sharing with assisted living facility

y = 3(4)ˣ + 45

The new graph will be shifted up by 45 units.

6. Fastest post

Amber's post travels the fastest.

After only two days, she already has more posts than anyone else.

By Day 10, she has more than 25 times the shares of her closest competitor.

7. Preference

It's not the number of friends you have, but the number of shares they make, that is the important factor.

Carter started with 10 friends, but they made only two shares.

Amber started with only three friends, but they made four shares. By Day 3, she had 192 shared compared to 82 for Carter and only 54 for Ben

If I had to choose, I would prefer a post with fewer friends initially but more shares, like Amber.