A certain colony of bacteria began with one cell, and the population tripled every 40 minutes. What was the population of the colony after 2 hours?

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We can approach this problem without setting up an exponential equation. Here's a simple table, which we make with mental math.

$$ \begin{array} {|c|c|} \hline \text{ population} & \text{time (minutes)} \\ \hline 1 & 0 \\ \hline 3 & 40 \\ \hline 9 & 80 \\ \hline 27 & 120 \\ \hline \end{array} $$

At 120 minutes (2 hours), the population is \(\boxed{27}\).

We can create a simple exponential equation:

$$ P = 1\cdot 3^t $$

Since we want for the population to triple every 40 minutes,

$$ P=1\cdot 3^{\frac{t}{40}} $$

There are 120 minutes in 2 hours:

$$ P = 1\cdot 3^{\frac{120}{40}} $$ $$ P=3^{3} $$ $$ P=\boxed{27} $$