To find A we use the initial condition; that is how many are at t=0. It becomes clear that N=A and so we let and define as the number at the start.
In your case you want to find k so rearranging my main equation gives
You could number crunch to find k but it can be simplified since and a factor of 1000 cancels to get
Now we have our constant we can find out a relationship between doubling time and the constant k.
From the first equation: at doubling time and so
In your case so which makes your answer almost correct, you just need a unit.
You can use the main equation for all these, just changing the values as necessary