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
[tex]\texttt{Common ratio = }\frac{1}{2}[/tex]
We have
[tex]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}[/tex]
Number of teams remaining after n rounds of play, p(n) = 2⁶⁻ⁿ
Here we need to find for what n p(n)=1
[tex]2^{6-n}=1\\\\2^{6-n}=2^0\\\\6-n=0\\\\n=6[/tex]
After 6 rounds one team will win.
