We’re being asked to calculate the percent of the original carbon-14 in the charcoal was present.

Recall that **radioactive/nuclear decay of isotopes **follows first-order kinetics and 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}$}\right.}{\mathbf{=}}\frac{\mathbf{ln}\mathbf{}\mathbf{2}}{\mathbf{k}}}$

The amount of carbon-14 present after t years is given by the exponential equation A_{t} = A_{0}ek_{t}, with k=- ln2/5600. Using carbon-14 dating of charcoal found along with fossilized leaf fragments, botanists arrived at an age of 48,000 years for a plant.

What percent of the original carbon-14 in the charcoal was present?

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