Why is it important in carbon dating to consider the ratio of carbon-14 atoms to other carbon atoms, rather than only the number of carbon-14 atoms?
Because C-14 = C-12 in living organisms, but C-14 < C-12 in nonliving organisms. Time of decay is a function of this ratio.
In living organisms, the C-14 to C-12 ratio is constant. However, in non-living organisms C-14 < C-12. Upon death C-14 begins to decay. Since all radio decay is 1st order kinetics, then the time for C-14 to decay to present day measurement is easily calculated from the 1st order decay equation