Question

An artifact was found and tested for its carbon-14 content. If 72% of the original carbon-14 was still present, what is its probable age (to the nearest 100 years)? (Carbon-14 has a half-life of 5,730 years).

Answer 1

2700 years

Explanation:

The exponential function for the fraction remaining is ...

r(t) = (1/2)^(t/5730)

where r is the remaining fraction and t is the time in years. We can solve for t to get ...

log(r) = (t/5730)log(1/2)

t = 5730·log(r)/log(1/2)

For the given r=0.72, the age of the artifact is estimated to be ...

t = 5730·log(0.72)/log(0.5) ≈ 2700 . . . years