Answer
$12,288$
Work Step by Step
Observing the number of bacteria after 0s, 5s, 10s, 15s,...
we define a sequence with
$a_{n}$ = the number of bacteria after $5(n-1)$ seconds.
$a_{1}=a=3$,
$a_{2}=3\cdot 2=a\cdot 2$,
$a_{3}=3\cdot 2^{2}=a\cdot 2^{2}$,
$a_{4}=3\cdot 2^{3}=a\cdot 2^{3}$,
$\ldots$.
We obtain a geometric sequence with $r=2$ and $a=3$.
$a_{n}=3\cdot 2^{n-1}$
So after $60=5(13-1)$ seconds,
the number of bacteria is
$a_{13}=3\cdot 2^{12}=12,288$.
