Question

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

a. Write a formula to model the number of teams remaining after any given round of play.

Answer 1

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

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