We carried out a direct dynamics study on the internal-energy dependence of the ensemble-averaged energy transfer moments of the isobutyl radical in collisions with N2 bath gas. We find a linear dependence of the downward moment ⟨ΔEd⟩ and the root-mean-square moment on the initial internal energy, but the upward moment ⟨ΔEu⟩ is found to be independent of the molecule's internal energy. We improved the exponential-down relaxation model by including a linear dependence of ⟨ΔEd⟩ on the initial energy, and we used the improved treatment in the 1D master equation for isobutyl radical decomposition reactions and for a model of competitive reactions with a larger difference in barrier heights. We calculated phenomenological rate constants and branching ratios from chemically significant eigenmodes of the master equation and showed that the energy dependence of ⟨ΔEd⟩ has a greater influence on channels with higher barriers in competitive reactions. Rate constants and branching ratios from master equation calculations indicate that for a given temperature and pressure, there is a constant ⟨ΔEd⟩ that can reproduce results obtained with an E-dependent ⟨ΔEd⟩. But a constant ⟨ΔEd⟩ cannot do this for all temperatures and pressures, with larger differences when the barriers for the competing channels differ more. We conclude that when the branching ratio of competitive reactions is sensitive to pressure, including the energy dependence of ⟨ΔEd⟩ in master equation simulations can make a significant difference in the results.