| Use the equation we have derived for carbon dating, N(t) = N0 e − 0.0001216 t,
to answer the following question. It may be helpful to know that the
half-life of 14C is 5700 years. |
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Problem 3- Calculate the initial amount of 14C in a fossil Approximately how many grams of 14C did an organism initially possess if there are 7 g remaining after 17,830 years? |
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Tutorial In this problem we are asked to solve for the initial quantity of 14C or N0. We write our model, N(t) = N0 e − 0.0001216 t. We know that 7 g remain after 17,830 years so we write,
Solving for N0 we have,
Therefore, an initial sample of approximately 61.2 g of 14C decays to 7 g after 17,830 years. Again, in terms of the half-life, this answer makes sense since 30.6 g would remain after 5700 years, 15.3 g would remain after 11,400 years, and 7.65 g would remain after 17,100 years.
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