Question

Radiocarbon measurements made in 1988 on the shroud of turin showed a decay rate of 14.2 disintegrations/min per gram of carbon. this is in comparison to the decay rate in the then current living organisms of 15.3 disintegrations/min per gram of carbon. given a half-life of 5730 years for carbon-14, what year is the artifact from?

Answer 1

We may use the equation:
A = A₀exp(-k*t)

Where k is the radioactive decay constant and related to half-life as:
t(half) = ln(2)/k

Substituting k from the second equation, and putting the values:

14.2 = 15.3 * exp(-ln(2)* t / 5,730)
t = 617 years

The artifact is 617 years old, which means it is from 1371.