SOLUTION: Which example below represents exponential decay? A. The balance on your city bus pass if you ride the bus twice a day every day. B. The number of views a popular (Tik Tok) g

Question 1182266: Which example below represents exponential decay?

A. The balance on your city bus pass if you ride the bus twice a day every day.
B. The number of views a popular (Tik Tok) gets over time
C. The number of teams competing as a tournament progresses
D. The growth of an invasive species of plants.
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Answer: Choice C
The number of teams competing as a tournament progresses

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Explanation:

We can rule out choices B and D since they represent growth functions. This is assuming that video's popularity keeps increasing. Though realistically there is likely a limit of some kind, and that applies to the growth of the plants as well. However, we'll just keep things relatively simple, or we'll just focus on a specific narrow window in time.

So we're between choices A and C now. Choice A represents decay but it's not exponential decay. The amount the balance goes down is the same per trip (assuming the bus company's prices don't change). That means choice A represents linear decay or linear decrease.

Choice C represents exponential decay. Why? Because the amount of teams left over gets cut in half when you advance to the next round. For instance, if you started with 64 teams in round 1, then round 2 will have 64/2 = 32 teams, and the next round will have 32/2 = 16 teams, and so on. We have 50% exponential decay happening. Half of the amount is lost when doing a transition. It might help to think of something like an NCAA March Madness bracket.

Side note: if you have n teams, then it takes rounds to declare a champion. Eg: if you have n = 64 teams, then it takes rounds to see who wins it all.

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