No, no. The equation for P = P(t) as a population that depends on time is
$\displaystyle P(t)=K\,n^{rt}.$
I've changed the small k to an r to avoid confusion. K, n, and r are constants. So, what is K for the first population?
You shouldn't feel stupid! K = 1000 is exactly correct. That tells you that the interpretation of K is that it is the initial population. So, perhaps a more telling modification of the original equation would be this:
$\displaystyle P(t)=P_{0}\,n^{rt}.$
Here $\displaystyle P_{0}=P(0),$ the initial population.
Ok. We've narrowed down our function by one constant. We now need to get a handle on n and r. You need to choose them such that $\displaystyle P(2)=2000,$ for the first colony. Also, you'd need $\displaystyle P(4)=4000, P(6)=8000,$ etc. How do you suppose you can do that?
Just out of curiosity, do you know about geometric progression and the formula for the nth term?
This might be an easier way for you to solve this problem, although I would advise that you try the method Ackbeet put forward because it helps you to think and construct your own equations.
You could actually write
$\displaystyle 2000=1000\,n^{2r},$ couldn't you? You know the population when $\displaystyle t=2:$ it's doubled from the initial population.
However, that's one equation with two unknowns. You'd like one more equation. How can you get it?