The age of an ancient artifact can be determined by the amount of radioactive carbon-14 remaining in it. If $D _ { 0 }$ is the original amount of carbon-14 and D is the amount remaining, then the artifact's age A (in years) is given by $A = - 8267 \ln \left( \frac { D } { D _ { 0 } } \right)$ Find the age of an object if the amount D of carbon-14 that remains in the object is 50% of the original amount $D _ { 0 }$
A) $4134 \mathrm { yr }$
B) $5730 \mathrm { yr }$
C) $2067 \mathrm { yr }$
D) $16400 \mathrm { yr }$
E) none of these

Question

Quizplus · Accepted Answer

If the amount of carbon-14 remaining is 50% of the original amount, then $\frac{D}{D_0}=0.5$. 
Substituting this into the equation, we get: 
$$A=-8267\ln\left(\frac{D}{D_0}\right)=-8267\ln(0.5)\approx 5730\text{ yr}$$
Therefore, the answer is choice B.

The Age of an Ancient Artifact Can Be Determined by the Amount