We present a simple growth model which was developed to explain Escherichia coli growth in batch culture. Optical density measurements are used to obtain E. coli growth curves for different inoculum sizes and nutrients concentrations. The model is described by two nonlinear mutually dependent differential equations that describe time evolution of bacteria and nutrients concentration. Introduction of the negative bacterium-bacterium interaction term is specific for the model and leads to the population decay. The proposed model describes entire experimental growth curves. The growth rate, as a function of initial nutrients concentration, follows the Monod function, whilst during the growth it decreases proportionally with the concentration of nutrients. The parameters in our equations can be related to the parameters of the logistic model. The proposed model can be applied to different E. coli strains and, because of the universality of the equations, might be applied to other bacterial strains.