If you have N

_{0} atoms of a radioactive

isotope at time 0, the number N which you have at time t is given by the equation:

N = N_{0} e^{-λ t}

Here lambda is the "decay constant", a measure of how fast the isotope decays. It is equal to (ln 2) divided by the half-life.

The equation above can be derived from the fact that since each atom of a radioactive isotope has an equal probability of decaying in a given time period, the rate of decay is proportional to the number of radioactive atoms present, i.e.:

dN/dt = -λ N.