PROBLEM SET 4, QUESTION 4:

Since the half-life of 14C is 6000 years, it would take 6000 years for the quantity of this isotope in the shinbone to be reduced by half. Assuming that the human had 8 micrograms when it died, it would have 4 micrograms 6000 years later. If we see 4 micrograms at the present time, it must have been 6000 years ago when it died.

Reasoning backward like this is the way observation of isotopes today can be used to deduce when something occurred in the past.