Carbon-14 commonly used for dating historical artifacts, is a radioactive isotope that is present in organic materials. Carbon-14 has a half-life of 5730 years.

Question

If a bone fragment is found that contains 70% of its original carbon-14,how old is the bone?

Answer 1

N(t) = N₀(2)^-t/thalf where N is the number of C-14 atoms and t and thalf are in years.

You are solving:

0.7 = 2^-t/5730 for t

take ln of both sides (log works too)

ln(.7) = -t/5730 * ln(2) using log rules for ln of exponential.

-5730*ln(.7)/ln(2) = t