Radioactive decay is an example of a first order process, although not chemical. Carbon-14 dating is a typical example of the use of a first order process to obtain information on the age of artifacts and organism's remains. The mathematical equations describing the decay of a radioactive substance is
where 
is the initial concentration of the radioactive
substance. A unimolecular decomposition such as
(this is one step in the thermal cracking of propane -- see Froment & Bischoff) is a first order reaction, and the equations describing the evolution of the 3 species involved are
together with initial values for the concentration of each species.
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