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(adsbygoogle = window.adsbygoogle || []).push({});

[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]

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# Model for series radioactive decay

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