We analyze a simple model for the copolymerization of two chemically distinct monomers that displays a wide variety of product sequence compositions depending on the rate coefficients for the stepwise addition of each monomer to a growing polymer chain. We show that in certain regions of parameter space the copolymer sequence composition depends sensitively on these parameter values, and we compute the information content of the resultant sequences. Finally, we show how the model may be used to interpret experimental data on copolymerization reactions.