A radioactive nuclide is produced at the constant rate of n per second (say, by bombarding a target with neutrons). The expected number N of radioactive nuclei in existence t seconds after the number is N0 is given by (λ = decay constant.

1
N = N0 e–λt
2
N = \(\frac{n}{\lambda}\) N0 e–λt
3
N = \(\frac{n}{\lambda}\) + \(\left(\mathrm{N}_0-\frac{n}{\lambda}\right)\)e–λt
4
N = \(\frac{n}{\lambda}\)\(\left(\mathrm{N}_0+\frac{n}{\lambda}\right)\)e–λt
5
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