Question

There are 64 teams at a volleyball tournament. Half of the teams are eliminated after each round. The function that models the number of teams left after x rounds is f(x) = 64(.5)x. Determine an appropriate domain for this model.

Answer 1

0 ≤ x ≤ 6

Explanation:

Both f(x) and x must be integer and both of them are greater than 0

Given:

• Half of the teams are eliminated after each round and the function is:

• f(x) = 64*
  `0.5^(x)`

It is a exponential function, so f(x) is going to reach 0 when x increases, so we can form the table of values:

x f(x)

0 64

1 32

2 16

3 8

4 4

5 2

6 1

Because this is a game, so we need only 1 team as the winner so that the domain of this function is:

0 ≤ x ≤ 6

Hope it will find you well

Answer 2

x ∈ ℤ

Explanation:

Both x and f(x) must be integers. For values of x greater than 6, fractional teams remain in the tournament, so we require x ≤ 6. It makes no sense to talk about negative numbers of tournament rounds, so the domain should probably be x ≥ 0. Hence, ...

... 0 ≤ x ≤ 6