4.05 algebra semester one
1. y = 2(3)ˣ; 2. y = 10(4)^x
Ben has 54 and 11 098; Carter = 80 and 10 249 shares;
Ben's function, the initial value of 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 it with 2 people each day, so b = 2.
Carter's function is y=10(2)ˣ
3. Graphs
The figure above shows the graphs for each function.
4. Predictions
(a) Amber
(l) Day 3: y = 3(4)³ = 3 × 64 = 192
(ll) Day 10: y = 3(4)¹⁰ = 3 × 1 048 576 = 3 145 728
(b) Ben
(l) Day 3: y = 2(3)³ = 2 × 27 = 54
(ll) Day 10: y = 2(3)¹⁰ = 2 × 29 049 = 118 098
(c) Carter
(l) Day 3: y = 10(2)³ = 10 × 8 = 80
(ll) Day 10: y =10(2)¹⁰ = 10 × 1024 = 10 240
Sharing with assisted living facility
y = 3(4)ˣ + 45
The new graph will be shifted up by 45 units.
5. The graph shifted up 45 shares; 6. Amber's;
6. Fastest post
Amber's post gets posted/travels/shares the fastest.
After only two days, she has more posts than anyone else.
By Day 10, she has more than 25 times the shares of her closest competitor.
7. I would prefer Fewer friends, but more shares.
Preference
It's not how many friends they have, but how many shares they do, that's the important factor, so if I had to choose, I would choose amber.
Carter started with 10 friends, but they made only two shares.
Amber started with just three friends, but they had four shares. On day three, she had 192 shares versus 82 for Carter and just 54 for Ben.
I would prefer a post with fewer friends initially, but more shares, like Amber.
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