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
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.
