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.
Carbon-14 decays almost completely within 100,000 years of the organism dying, and many fossils and rock strata are hundreds of times older than that.
To date older fossils, other methods are used, such as potassium-argon or argon-argon dating.
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.