Question

64 teams participate in a softball tournament in which half the teams are eliminated after each round of play.

c. How many rounds of play will it take to determine which team wins the tournament?

Answer 1

After 6 rounds one team will win.

Explanation:

This is an example of geometric progression,

Let p(n) represents the number of participants remaining after n rounds of play.

First term = 64

`\texttt{Common ratio = }(1)/(2)`

We have

`p(n)=a* r^(n)\\\\p(n)=64* \left ((1)/(2) \right )^(n)=2^(6)* \left ((1)/(2) \right )^(n)\\\\p(n)=2^(6-n)`

Number of teams remaining after n rounds of play, p(n) = 2⁶⁻ⁿ

Here we need to find for what n p(n)=1

`2^(6-n)=1\\\\2^(6-n)=2^0\\\\6-n=0\\\\n=6`

After 6 rounds one team will win.