- #1
KFC
- 488
- 4
If nucleus A decays to nucleus B in rate a, and B decays to C in rate b, and C is decaying at the rate c. To setup a model for that process, we start from A
[tex]
\frac{dA}{dt} = - a A(t)
[/tex]
and for B, part for B is dying out from it's own decaying process but some amount of A will decay into B, so
[tex]
\frac{dB}{dt} = a A(t) - bB(t)
[/tex]
But for C, it is quite confusing, the total number of C is proportional to the number of B directly but also to that of A indirectly, of course it will dying out due to it's own decaying process. My question is should I include a term for A(t) in the different equation for C? That is, should I write
[tex]
\frac{dC}{dt} = a A(t) + bB(t) - cC(t)
[/tex]
or
[tex]
\frac{dC}{dt} = bB(t) - cC(t)
[/tex]
[tex]
\frac{dA}{dt} = - a A(t)
[/tex]
and for B, part for B is dying out from it's own decaying process but some amount of A will decay into B, so
[tex]
\frac{dB}{dt} = a A(t) - bB(t)
[/tex]
But for C, it is quite confusing, the total number of C is proportional to the number of B directly but also to that of A indirectly, of course it will dying out due to it's own decaying process. My question is should I include a term for A(t) in the different equation for C? That is, should I write
[tex]
\frac{dC}{dt} = a A(t) + bB(t) - cC(t)
[/tex]
or
[tex]
\frac{dC}{dt} = bB(t) - cC(t)
[/tex]