Problem 4 - Calculate the age of a fossil

If 12% of the initial amount of ¹⁴C in a sample remains, how much time has elapsed?

Tutorial

We are given that 12% of the initial sample remains after some amount of time, say τ. If the initial sample is N₀ g, then τ years later there will be 12% of N₀ or 0.12N₀. We write,

N(τ) = (0.12)N₀ = N₀ e ^{− 0.0001216τ} .

Canceling N₀ on both sides of the equation and solving for τ yields,

Therefore, after approximately 17,436 years, 12% of the initial sample remains. Notice that we did not need to know how much ¹⁴C was contained in our original sample. We only needed to know that a certain percentage of it remained.

Our answer makes sense since 50% would remain after 5700 years, 25% would remain after 11,400 years, and 12.5% would remain after 17,100 years.