We are asked to determine the age of a bone sample using carbon dating given that carbon-14 decays with first-order kinetics and a half-life of 5730 years and that a bone from an ancient human contains 15.5 % of the C-14 found in living organisms.

Recall that ** half-life** is the time needed for the amount of a reactant to decrease by 50% or one-half. The half-life of a first-order reaction is given by:

$\overline{){{\mathbf{t}}}_{\raisebox{1ex}{$\mathbf{1}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{2}$}\right.}{\mathbf{=}}\frac{\mathbf{ln}\mathbf{2}}{\mathbf{k}}}$

Anthropologists can estimate the age of a bone or other sample of organic matter by its carbon-14 content. The carbon-14 in a living organism is constant until the organism dies, after which carbon-14 decays with first-order kinetics and a half-life of 5730 years. Suppose a bone from an ancient human contains 15.5 % of the C-14 found in living organisms.

How old is the bone?

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