System theory is classically applied to describe and to predict the effects of training load on performance. The classic models are structured by impulse-type transfer functions, nevertheless, most biological adaptations display exponential growth kinetics. The aim of this study was to propose an extension of the model structure taking into account the exponential nature of skeletal muscle adaptations by using a genetic algorithm. Thus, the conventional impulse-type model was applied in 15 resistance trained rodents and compared with exponential growth-type models. Even if we obtained a significant correlation between actual and modelled performances for all the models, our data indicated that an exponential model is associated with more suitable parameters values, especially the time constants that correspond to the positive response to training. Moreover, positive adaptations predicted with an exponential component showed a strong correlation with the main structural adaptations examined in skeletal muscles, i.e. hypertrophy (R ²  = 0.87, 0.96 and 0.99, for type 1, 2A and 2X cross-sectional area fibers, respectively) and changes in fiber-type composition (R ²  = 0.81 and 0.79, for type 1 and 2A fibers, respectively). Thus, an exponential model succeeds to describe both performance variations with relevant time constants and physiological adaptations that take place during resistance training.