A goal of introductory physics for life sciences (IPLS) curricula is to prepare students to effectively use physical models and quantitative reasoning in biological and medical settings. To assess whether this goal is being met, we conducted a longitudinal study of the impact of IPLS on student work in later biology and chemistry courses. We report here on one part of that study, a comparison of written responses by students with different physics backgrounds on a diffusion task administered in a senior biology capstone course. We observed differences in student reasoning that were found to be associated with prior or concurrent enrollment in IPLS. In particular, we found that IPLS students were more likely than non-IPLS students to reason quantitatively and mechanistically about diffusive phenomena, and to successfully coordinate between multiple representations of diffusive processes, even up to two years after taking the IPLS course. Finally, we describe methodological challenges encountered in both this task and other tasks used in our longitudinal study.