Answer:
An elimination chess tournament has half the number of players in successive round.
Explanation:
So exponential decay, can be expressed in an exponential equation:
where b can be defined as:
, where r is positive and represents the decay.
This decay is constant, but the amount decreased is not constant.
this is because let's say you have a decay of 50% which is constant, well if you have 100 people, then a decay of 50%, would result in losing half or 50 people.
Now the second time this occurs you only have 50 people so a decay of 50% would would result in losing half or 25 people.
See how the second time, the decay is still 50%, but the second time the amount of people only decreased by 50, and the second time it decreased by 25, which is less than the first time.
So let's look at each option
A backgammon competition has 10 players exiting after each round of of games. This is not the answer, because as mentioned before the amount lost is not constant, but rather the percentage is constant.
An elimination chess tournament has half the number of players in successive round. This is the answer, because it has a constant decay of 50%.
We already found the answer but let's look at the other options.
A table tennis club has 10, 9, 8 new members in three years respectively. This cannot be represented using exponential decay, since the equation would need f(1) = 10, f(2) = 9, f(3) = 8, which appears to represent a linear relationship, rather than an exponential decay.
A billiards organization lost 5%, 4%, and 3% of its members in three years respectively. This is wrong because as mentioned before, the percentage of decay is constant, while the amount isn't, except here it's explicitly giving us the percentage of decay which is changing year to year.