A mathematical model is presented for the increase and decrease of non-inherited antibiotic resistance levels in bacteria. The model is applied to experimental data on E. coli exposed to amoxicillin or tetracyclin in different concentrations. The parameters of the model are estimated using a Monte Carlo Markov Chain method. The model accurately describes build-up and decline of antibiotic resistance caused by physiological adaptations as long as no genetic changes have occurred. The main conclusion of the analysis is that short time periods are sufficient to re-obtain low MIC-values after long-lasting exposure to these antibiotics.