Differential equations? Or difference equations? Your approach is rather like a Markov chain; it could well be a valid approach, but I don't see any derivatives in there. In any case, how did you get this line:
A radioactive isotope A decays at the rate of 2% per century into a second radioactive isotope B, which in turn decays at a rate of 1% per century into a stable isotope C.
a) Find a system of linear differential equations to describe the decay process. If we start with pure A, what are the proportions of A, B and C after 500 years, after 1,000 years and after 1,000,000 years?
This is what I've done so far:
Let
I'm not too sure if I'm correct, I think the eigenvalues are
At 500 years:
Is what I'm doing correct so far?