Keyword: «unified state exam in mathematics»

The article is devoted to the problem of constructing a mathematical model of an economic problem at the unified state exam in mathematics (profile level). In order to develop the creative and creative thinking of schoolchildren, it is proposed to build several alternative models of the situation and analyze their capabilities.

In many practical applications, relationships between the quantities under consideration can be expressed as a functional relationship. If a functional relationship is established between the quantities under consideration, the properties of the resulting function can be used to study the dynamics of change in the quantities under consideration. Furthermore, by establishing a functional relationship between the quantities under consideration, the problem can be visualized by constructing a function graph or a table of function values. Since the quantities arising when solving compound interest problems can be viewed as discrete functions of the interest rate, the entire process of studying the problem and finding solutions is easily understood by first constructing a table of the values of the desired function, clearly (visually) showing the dynamics of the increase (decrease) in the quantity under consideration depending on the interest rate. In recent years, problems involving compound interest have become mandatory in the exam questions offered on the Unified State Exam in Mathematics (advanced level). We hope that the functional approach to solving compound interest problems developed in this article will be useful for both general education school teachers and high school graduates preparing for the Unified State Exam in Mathematics (advanced level). The article's presentation is constructive, meaning the authors' proposed method for solving this class of problems is illustrated with specific examples involving compound interest.