Approximately 28650 years.
Assumptions.
1. All of the Nitrogen-14 came from decay of Carbon-14
2. The lifespan of the animal which the bone came from is insignificant compared to the age of the bone. This is because there will be carbon-14 decay happening during the lifetime of the animal.
So the original amount of carbon-14 will be the sum of the masses of carbon-14 and nitrogen-14. So that is
3.875 g + 120.125 g = 124 g originally
Divide the original amount of Carbon-14 by the amount of carbon-14 remaining, getting
124 / 3.875 g = 32
Calculate the base 2 logarithm of the ratio to determine how many half lives expired.
ln(32)/ln(2) = 3.46574 / 0.693147 = 5
So 5 half lives have expired. Now simply multiply by the duration of a half life. So
5 * 5730 years = 28650 years
