College Math
posted by Yvonne on .
An artifact was found and tested for its carbon14 content. If 88% of the original carbon14 was still present, what is its probable age (to the nearest 100 years)? Use that carbon14 has a halflife of 5,730 years.

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.