A previously proposed reptation model is used to interpret exponential shear flow data taken on an entangled polystyrene solution. Both shear and normal stress measurements are made during exponential shear using mechanical means. The model is capable of explaining all trends seen in the data, and suggests a novel analysis of the data. This analysis demonstrates that exponential shearing flow is no more capable of stretching polymer chains than is inception of steady shear at comparable instantaneous shear rates. In fact, all exponential shear flow stresses measured are bounded quantitatively by stress measurements taken during inception of steady shear. Information taken from the model about chain stretching suggests that normal stress measurements are strong indications of stretching, whereas shear stress measurements are indicative of both chain stretching and segment orientation.