We’re being asked to **determine the age of the fossil** containing an eighth as much carbon-14 of a living animal.

Recall that * radioactive/nuclear decay of isotopes* follows first-order kinetics, and the integrated rate law for first-order reactions is:

$\overline{){\mathbf{ln}}{\left[\mathbf{N}\right]}_{{\mathbf{t}}}{\mathbf{=}}{\mathbf{-}}{\mathbf{kt}}{\mathbf{+}}{\mathbf{ln}}{\left[\mathbf{N}\right]}_{{\mathbf{0}}}}$

where:

[N]_{t} = concentration at time t

k = decay constant

t = time

[N]_{0} = initial concentration.

If a fossil bone is found to contain an eighth as much as C-14 as the bone of a living animal, what is the approximate age of the fossil? (Half-life of C-14 = 5715 years)

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