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Some isotopes have half lives longer than the present age of the universe, but they are still subject to the same laws of quantum physics and will eventually decay, even if doing so at a time when all remaining atoms in the universe are separated by astronomical distances.

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Symbolically, the process of radioactive decay can be expressed by the following differential equation, where N is the quantity of decaying nuclei and k is a positive number called the exponential decay constant.

The meaning of this equation is that the rate of change of the number of nuclei over time is proportional only to the number of nuclei.

This is consistent with the assumption that each decay event is independent and its chance does not vary over time.

where is the half-life of the element, is the time expired since the sample contained the initial number atoms of the nuclide, and is the remaining amount of the nuclide.

This leaves out important information which would tell you how precise is the dating result.