Answer
$12,288$ bacteria
Work Step by Step
The problem can be modeled using a geometric sequence. Let $\{a_n\}$ the number of bacteria after $n-1$ sets of $5$ seconds. The elements of the sequence are:
$$\begin{cases}
a_1=3\\
r=2.
\end{cases}$$
The $n$th term is
$$a_n=a_1r^{n-1}=3(2^{n-1}).$$
In one minute there are $60/5=12$ sets of $5$ seconds. The number of bacteria after one minute is $a_{13}$:
$$a_{13}=3(2^{12})=12,288.$$