Tutorial to help you answer this question
|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.
Problem 5- Calculate the amount of 14C remaining after a given time has passed
Approximately what percentage of an initial sample of 14C remains after 33,450 years?
In this problem we would like to know the percentage of the initial sample that remains after 33,450 years.
Fortunately, we do not need to know how much 14C there was to begin with. We write the year t = 33,450 years into our model,
N(33450) = N0 e (−0.0001216)· (33450) ≈ 0.017N0.
Because the coefficient on N0 is 0.017, we conclude that approximately 1.7% of the initial sample remains after 33,450 years.
This makes sense since 50% would remain after 5700 years, 25% would remain after 11,400 years, 12.5% would remain after 17,100 years, 6.25% would remain after 22,800 years, 3.125% would remain after 28,500 years, and 1.5625% would remain after 34,200 years.