# Carbon dating using exponential growth

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The basic equation of radiometric dating requires that neither the parent nuclide nor the daughter product can enter or leave the material after its formation.

If we assume Carbon-14 decays continuously, then $$C(t) = C_0e^,$$ where $C_0$ is the initial size of the sample. Since it takes 5,700 years for a sample to decay to half its size, we know $$\frac C_0 = C_0e^,$$ which means $$\frac = e^,$$ so the value of $C_0$ is irrelevant.

Alternatively, if several different minerals can be dated from the same sample and are assumed to be formed by the same event and were in equilibrium with the reservoir when they formed, they should form an isochron. In uranium–lead dating, the concordia diagram is used which also decreases the problem of nuclide loss.

Finally, correlation between different isotopic dating methods may be required to confirm the age of a sample.

The method compares the abundance of a naturally occurring radioactive isotope within the material to the abundance of its decay products, which form at a known constant rate of decay.

and is now the principal source of information about the absolute age of rocks and other geological features, including the age of fossilized life forms or the age of the Earth itself, and can also be used to date a wide range of natural and man-made materials.