Question

In a large single-elimination basketball tournament, the first round of play begins with 64 teams. In each successive round, the number of teams remaining in the tournament is reduced by half. This relationship can be described by the following exponential function.

Answer 1

f(n)=f(n-1)÷2

Explanation:

Answer 2

`T_(n)=64((1)/(2))^(n-1)` defines the relationship.

Explanation:

In a large single elimination basketball tournament, the first round of the play begins with 64 teams.

In each successive round, the number of teams remaining in the tournament is reduced by half.

So the sequence formed will be 64, 32, 16, 8........

Now we have to find the relationship.

In the sequence there is a common ratio of
`(1)/(2)` in each successive term

r =
`\frac{\text{2nd term}}{\text{1st term}}=(64)/(32)=2`

Since explicit formula of an exponential sequence is

`T_(n)=a(r)^(n-1)`

`T_(n)=64((1)/(2))^(n-1)`

Therefore, equation representing the relationship will be

`T_(n)=64((1)/(2))^(n-1)`