# Carbon dating mathematical modelling

*06-Mar-2019 14:47*

Methods for the analysis of the concentration-time curves with mathematical models describing the physiological processes and the appropriate anatomy are now available to give a quantitative portrayal of both structure and function: such is the approach to metabolic or functional imaging.One formulates a model first by defining what it should represent: this is the hypothesis.We have negotiated special rates with reputable radiocarbon laboratories which allows us to provide exceptional value for money.For more details please contact one of our senior archaeologists using this link.In the previous article, we saw that light attenuation obeys an exponential law.To show this, we needed to make one critical assumption: that for a thin enough slice of matter, the proportion of light getting through the slice was proportional to the thickness of the slice.

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.

This question can be answered using a little bit of calculus. Once we have an expression for t, a "definite integral" will give us the mean value of t (this is how "mean value" is defined).

From the equation above, taking logarithms of both sides we see that lt = -ln(N/N.

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.

Exactly the same treatment can be applied to radioactive decay.