Question

1. Write an exponential function to represent the spread of Ben's social media post. 2. Write an exponential function to represent the spread of Carter's social media post. 3. 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. 4. 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. 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) + 45. How does this graph compare with the original graph of Amber's photo share? 6. Based on your results, which students' post travels the fastest? How is this shown in the equation form of the functions? 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.

Answer 1

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

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 shares 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.