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By "age" we mean the elapsed time from when the mineral specimen was formed.

Radioactive elements "decay" (that is, change into other elements) by "half lives." If a half life is equal to one year, then one half of the radioactive element will have decayed in the first year after the mineral was formed; one half of the remainder will decay in the next year (leaving one-fourth remaining), and so forth.

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.

Various elements are used for dating different time periods; ones with relatively short half-lives like carbon-14 (or C) are useful for dating once-living objects (since they include atmospheric carbon from when they were alive) from about ten to fifty thousand years old. Longer-lived isotopes provide dating information for much older times.

Although the time at which any individual atom will decay cannot be forecast, the time in which any given percentage of a sample will decay can be calculated to varying degrees of accuracy.

The time that it takes for half of a sample to decay is known as the half life of the isotope.

Carbon-14 dating can be used on objects ranging from a few hundred years old to 50,000 years old.

Given isotopes are useful for dating over a range from a fraction of their half life to about four or five times their half life.

It is one of the simplest examples of a differential equation.

How radiometric dating works in general Why methods in general are inaccurate Why K-Ar dating is inaccurate The branching ratio problem How Errors Can Account for the Observed Dates Why older dates would be found lower in the geologic column especially for K-Ar dating Do different methods agree with each other on the geologic column?

Since there is now only 1/4 of the original amount of Parentium-123, we know that two half-lives of Parentium-123 have elapsed.

But there are some questions that come to mind: Calculus students typically meet this problem somewhere in the second semester.

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