Question

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

Answer 1

Answer:

After 6 rounds one team will win.

Step-by-step 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

$\texttt{Common ratio = }\frac{1}{2}$

We have

               $p(n)=a\times r^{n}\\\\p(n)=64\times \left (\frac{1}{2} \right )^{n}=2^{6}\times \left (\frac{1}{2} \right )^{n}\\\\p(n)=2^{6-n}$

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.