if the colony is tripling every 30mins, that simply means is "increasing at a rate of 200%", so, whatever the current is, plus 200% of that, which makes it 300% or a tripling rate
now, from noon to 3pm, there are 6 half-hours, so it has gone through that cycle 6 times already, or 6 periods
[tex]\bf \qquad \textit{Amount for Exponential change}\\\\
A=P(1\pm r)^t\qquad
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{starting amount}\to &2\\
r=rate\to 200\%\to \frac{200}{100}\to &2.00\\
t=\textit{elapsed period}\to &6\\
\end{cases}
\\\\\\
A=2(1+2.00)^6[/tex]
