Consider a radiactive decay problem involving two types of nuclei, A and B, with populations Na(t) and Nb(t). Suppose that type A nuclei decay to form type B nuclei, which then also decay, according to differential equations:
dNa/dt = - Na/Ta
dNb/dt = Na/Ta - Nb/Tb
where Ta and Tb are the decay constants. Na(0) = 100 and Nb(0) = 0.
The Attempt at a Solution
I solved the equation for Na(t) and got 100*e^(-t/Ta), but I'm not sure about Nb. Intuitively, I think it has to be something like:
100*(1 - e^(-t/Ta))*e^(-t/Tb)
but I know this is wrong