The student uses correct mathematical notation, symbols, and terminology consistently throughout the IA, effectively presenting formulas for logistic and cubic functions. Key terms and variables are clearly defined when first introduced, and the main concepts are thoroughly described in the introduction, emphasizing the implications of Germany's population structure. The student employs multiple forms of mathematical representation, such as formulae, tables, and graphs, to enhance the analysis, and explains all mathematical calculations in detail. However, the degree of accuracy for rounded values is not specified, and the graphs, tables, and diagrams are not labeled appropriately. Overall, the student demonstrates a strong understanding of mathematical concepts, though there are areas for improvement in accuracy and labeling.