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The carbon-14 decays with its half-life of 5,700 years, while the amount of carbon-12 remains constant in the sample.By looking at the ratio of carbon-12 to carbon-14 in the sample and comparing it to the ratio in a living organism, it is possible to determine the age of a formerly living thing fairly precisely. So, if you had a fossil that had 10 percent carbon-14 compared to a living sample, then that fossil would be: t = [ ln (0.10) / (-0.693) ] x 5,700 years t = [ (-2.303) / (-0.693) ] x 5,700 years t = [ 3.323 ] x 5,700 years Because the half-life of carbon-14 is 5,700 years, it is only reliable for dating objects up to about 60,000 years old.

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It then takes the same amount of time for half the remaining radioactive atoms to decay, and the same amount of time for half of those remaining radioactive atoms to decay, and so on. The amount of time it takes for one-half of a sample to decay is called the half-life of the isotope, and it’s given the symbol: It’s important to realize that the half-life decay of radioactive isotopes is not linear.

For example, you can’t find the remaining amount of an isotope as 7.5 half-lives by finding the midpoint between 7 and 8 half-lives.

However, the principle of carbon-14 dating applies to other isotopes as well.

Potassium-40 is another radioactive element naturally found in your body and has a half-life of 1.3 billion years.

Ar (argon), the atom typically remains trapped within the lattice because it is larger than the spaces between the other atoms in a mineral crystal.

But it can escape into the surrounding region when the right conditions are met, such as change in pressure and/or temperature.

Potassium–argon dating, abbreviated K–Ar dating, is a radiometric dating method used in geochronology and archaeology.

It is based on measurement of the product of the radioactive decay of an isotope of potassium (K) into argon (Ar).

In his article Light Attenuation and Exponential Laws in the last issue of Plus, Ian Garbett discussed the phenomenon of light attenuation, one of the many physical phenomena in which the exponential function crops up.

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