User:Vsmith/Dating calc

For radioactive decay The relationship between fraction remaining (f) and the number of half-lives (n) elapsed can be shown by: Therefore the fraction remaining after time n is: f=1/2n which is equivalent to f=(1/2)n or f=0.5n. This makes the calculation of the age if the fraction remaining is known quite simple. Solving the above relationship for n using the properties of logarithms:


 * f=0.5n becomes
 * ln f = n&middot;ln 0.5 and
 * $$ n = \frac{\ln \left({f}\right)}{\ln \left({0.5}\right)}$$

As an example, for a sample that contains 0.06780 of the original C-14:
 * $$ n = \frac{\ln \left({0.06780}\right)}{\ln \left({0.5}\right)}$$ solving gives n= 3.88 half lives and
 * 3.883 half lives * 5730 yrs/half life = 22,250 yrs.

A more simple example, for a sample containing 0.25 of the original:
 * $$ n = \frac{\ln \left({0.25}\right)}{\ln \left({0.5}\right)}$$ solving gives n= 2 half lives and
 * 2 half lives * 5730 yrs/half life = 11460 yrs.