Posted:

**Aug 26, 2011 11:28 pm**Calilasseia wrote:Plus, strictly speaking, decay rates over the long term aren't 'constant', they obey an exponential decay law.

Strictly speaking that´s wrong. Rates are expected numbers per unit time (wiki says probabilities, but that´s merely the special case where the random variable is an index function of an event). If you have a process where events occur both continuously and with a constant rate, then the waiting time between two events follows an exponential distribution and so does the waiting time for the first event from an arbitrary starting time. The activity of a particular ammount of radioactive material follows an exponential decay law, because in this case we are looking at the waiting times for the first events (decays) and these are exponentially distributed. This then leads to an exponentially decreasing number of expected decays per unit time and if the ammount of the substance is high the law of large number provides an approximately deterministic law.

You seem to mix up the decay rate with the expected activity and the observed activity there.

Note: Rates are often not constant in similar processes. An example are mutation and fixation rates for substitutions used in molecular clock estimates for divergence dates. That´s why they have to be callibrated using fossils and preferably a lot of them - this allows you to track the way these rates have changed over time and thus calculate divergence dates.