Carbon dating mathematical modelling

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Modern imaging techniques can provide sequences of images giving signals proportional to the concentrations of tracers (by emission tomography), of X-ray-absorbing contrast materials (fast CT or perhaps NMR contrast), or of native chemical substances (NMR) in tissue regions at identifiable locations in 3D space.

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.

In this second article he describes the phenomenon of radioactive decay, which also obeys an exponential law, and explains how this information allows us to carbon-date artefacts such as the Dead Sea Scrolls.

We end up with a solution known as the "Law of Radioactive Decay", which mathematically is merely the same solution that we saw in the case of light attenuation.

We get an expression for the number of atoms remaining, N, as a proportion of the number of atoms N, where the quantity l, known as the "radioactive decay constant", depends on the particular radioactive substance.

We can easily find an expression for the chance that a radioactive atom will "survive" (be an original element atom) to at least a time t.

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