Answer
A) $N(r) = 64\cdot (0.50)^r$
B) 6 rounds.
Work Step by Step
Data.
\begin{equation}
\begin{aligned}
a&= 64\\
i&= 50\% = 0.50\\
b&=1-i= 0.5
\end{aligned}
\end{equation}
A) A model of the number of team remaining can be written as:
\begin{equation}
\begin{aligned}
N(r)&=a\cdot b^r\\
&=64\cdot (0.50)^r
\end{aligned}
\end{equation} B)
Use
$r=\log_{0.50}(N(r)/64)$
\begin{equation}
\begin{aligned}
r&=\log_{0.50}(N(r)/64)\\
&= \log_{0.50}(1/64)\\
&= 6
\end{aligned}
\end{equation}
The team went through 6 rounds.
