The late Eocene Epoch falls in the Cenozoic Era, which is the most recent geologic period. The time at which the Dorudon whale was alive can be determined by studying fossils found in the layers of rock that were formed during the Eocene Epoch. Fossils are studied to determine the age of the organism, as well as its habitat and behavior. Additionally, analysis of chemical isotopes in the fossils can also provide clues about the climate and environment in which the organism lived.