So, a scientist is growing a colony of bacteria. After 2 hours, there are 40 bacteria. After 3 hours, there are 120 bacteria. If the population of bacteria grows exponentially, then how many bacteria will there be after 4 hours?

We have (2, 40), (3, 120), and we need to find (4, ?). I've done the following:

$\displaystyle 40=ae^2k$, and $\displaystyle 120=ae^3k$

2) $\displaystyle a=40/e^2k$

3) $\displaystyle 120/40=(40/e^2k)e^3k$

4) $\displaystyle 3=3^3k/e^2k$

That's where I am. In most of the examples I've seen, in step 3, the equation is usually being multiplied by something simple, like $\displaystyle e^4k/e^2k$, but for this one, I guess I have to divide $\displaystyle e^3k/e^2k$, which in step 4, I am confused.