How would i do this, Help! Please and thank you:)

Question

Testing shows that a sample of wood from an artifact contains 50% of the original amount of carbon-14. Given that the half-life of carbon-14 is 5730 years, how old is the artifact?
\l "\l " A. 11,460 years

\l "\l " B. 11,460 years

\l "\l " C. 5730 years

\l "\l " D. 22,920 years

Answer 1

The amount obeys an exponential decay law:

 

N(t) = N(0)e^-kt

 

Given a half-life T = 5730 years,

 

e^-kT = 1/2

 

k = - ln(1/2) / T = - ln(1/2) / 5730 = 1.209681 x 10^-4 years^-1

 

Since the amount present dropped to 50% (i.e. 1/2 of the initial amount), then one half-life has elapsed, so the age is 5730 years.