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:
The amount of carbon-14 present after t years is given by the exponential equation At = A0ekt, 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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