An artifact was found and tested for its carbon-14 content. If 88% of the original carbon-14 was still present, what is its probable age (to the nearest 100 years)? Use that carbon-14 has a half-life of 5,730 years.

Answer 1

If you start with amount P, then after t years, R, the fraction remaining, is

R = 2^(-t/5730)

See how that works? Every 5730 years, the power of 2 goes down by 1.

2^(-t/5730) = .88
-t/5730 = ln(.88)/ln(2) = −0.321928095
t = 5730 * 0.321928095
t = 1844.64798435
or, to the nearest 100 years, 1800.