How Do You Calculate the Amounts of B and C in Radioactive Decay Over Time?

[elsen_678]

hi I'm new here hope you can help me with this problem
nuclei A decays to B and then to C(stable)
A and B have the same decay constant, n
Initially the amount of A is N(0)>0 while B and C are zero
then the amount of A at any time is :
N(t)=N(0)exp(-nt)
can somebody derive the equation for the amount of sample B and C as a function of time ?
thanks

 

[mathman]

If you have any exposure to elementary diff. eq., the set up is as follows:

B'(t)=n(A(t)-B(t))
C'(t)=nB(t)
where A(t)=A(0)exp(-nt)