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

Multiple Choice

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