The half-life of carbon-14 is 5,600 years.A fossil that has one-eighth the normal proportion of carbon-14 to carbon-12 is probably
A)2,800 years old.
B)5,600 years old.
C)11,200 years old.
D)16,800 years old.
E)22,400 years old.

Question

Quizplus · Accepted Answer

The fact that the fossil has one-eighth the normal proportion of carbon-14 to carbon-12 means that it has gone through three half-lives of carbon-14 decay. Therefore, we can use the formula for exponential decay: 
N=N0e^(-kt), where N is the final amount, N0 is the initial amount, k is the decay constant (ln2/t1/2 for carbon-14), and t is time. 
We can simplify this equation to: 
N/N0=1/2^t/t1/2 
Since the fossil has one-eighth the normal proportion, N/N0=1/8, and we can solve for t: 
1/8=1/2^3 
t=3t1/2 
Since the half-life of carbon-14 is 5,600 years, we can determine that: 
t=3(5,600)=16,800 years

The Half-Life of Carbon-14 Is 5,600 Years