The aim of this paper is to suggest the expansion of learning materials designed for university teachers who work with students who have chosen advanced mathematics as an elective, or with high school students who are engaged in mathematics beyond compulsory curriculum. Students will work with examples of mathematical models of simple but real problems. From a certain perspective on solving simple tasks, we can get to concepts such as the fixed points or the attracting orbits and even chaos. Lectures are conducted in such a way that students understand the basic concepts by analysis of graphs associated with these problems. We deliberately chose a topic that is not normally part of lessons and could make mathematics or computer science more varied. Another of the reasons for writing this paper is the gradual discovery of the fact that students have increasingly difficulties with reading the graph and understanding the connection of the graph and the real situation at all. This is an issue that is up to date, it could make mathematics or informatics more interesting, and it certainly deserves attention.