This paper proposes modelling based learning as a tool for learning and teaching mathematics. The example of modelling real world problems leading to the exponential function as the solution of differential equations is described, as well as the observations about students' activities during the process. The students were acquainted with the differential equations for the very first time and it was interesting to approach this topic in a new way by modelling. In this process students were encouraged to use educational software GeoGebra in order to develop ability to solve a problem connected with the real world and differential equations. The modelling process in mathematical education tends to follow the didactical cycle of activities and reach a desirable level of accomplishments of students' activities and competencies. (Contains 4 figures and 1 table.)