How the fuck do you know what is in the barrel after 1 year? Or 10 years, or 5000 years?
And how do you know how radioactive it will be at any given time?
This is where the Bateman equations come in. With these equations you can say exactly what's in that barrel at any given time, even if the decay chain is 10 or 15 stages long. All you need to know is the decay constant of every compound in the decay chain (common knowledge) and how much you put in the first place (hurr).
Here they are:
am(t) = Ni°∑ cime-λit
cim = Πj=1m λj / Πj=1;j≠im (λj - λi)
m being the compound, λ being the decay constant, Ni° being the initial number of nuclei in the barrel.
Sorry they look like shit, was too lazy to make a fancy PNG file with it laid out nicely. It was about time I started the "science" part of this blog so here it is. Hope you're having a nice week.