![t(n)=64((1)/(2))^n](https://img.qammunity.org/2023/formulas/mathematics/college/ptzvq4gwejfy9cy4d6hrqhndsnsuuhfo7m.png)
1) The best way to tackle this question, is after writing out a function testing them.
2) Consider that the initial number of teams is 64. And as each match has only one winner, then each round presents half of the number of the teams this way up to the final match when there will be only one champion.
3) So, let's write it:
![\begin{gathered} y=a(b)^n \\ t(n)=64((1)/(2))^n \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/l14kxtle2bmowuwi88od9457q26wi2tlsp.png)
4) Note that we can see that each round
1st round: 64
2nd round: 32
3rd round: 16
And so on.