Need some help on a homework problem:
At time t = 0 a vessel is initially loaded with 1 kg. of pure Lead-214, which subsequently decays to Bismuth-214 and Polonium-214. Let L, B, and P denote the decay constants for these 3 elements.
Write a system of equations that gives the amounts of these 3 elements over time, and solve the system exactly.
I know the equation for the decay of a radioactive element is so I have the equation for Lead-214:
x(t) = 1 kg. * e ^ (-L * t)
I can't figure out the equations for the other two elements though. I do know Lead-214 decays to Bismuth-214 which decays to Polonium-214.
Any help would be awesome.