This work presents a multi-route, non-structured kinetic model for determination of microbial growth and substrate consumption in an experimental batch bioreactor in which beta-galactosidase is produced by Kluyveromyces marxianus growing on cheese whey. The main metabolic routes for lactose, and oxygen consumption, cell growth, and ethanol production are derived based on experimental data. When these individual rates are combined into a single growth rate, by rewriting the model equations, the model re-interpretation has a complexity similar to that of the usual variations of the Monod kinetic model, available in the literature. Furthermore, the proposed model is in good agreement with the experimental data for different growth temperatures, being acceptable for dynamic simulations, processes optimization, and implementations of model-based control technologies.