Representing Exponential Decay Graphically with Local Rate (Tangent Insight)

This example demonstrates how to model and visualize exponential decay as a mathematical phenomenon, and how to use local geometric information—such as tangents—to interpret how the rate of decrease changes with the input variable. The core concepts include exponential functions for modeling decay, graph-based understanding of function behavior, and the connection between tangents and derivatives as a representation of local change rate. Construction-wise, the GeoGebra setup is driven by the key objects listed in the construct summary (A1, A2, B1, C1, D1, E1, F1), which typically correspond to the main curve/function representation, supporting points, and auxiliary elements like tangent lines used to highlight local behavior. The activity is well-suited for late secondary school through early undergraduate students, particularly for calculus introduction, function graphing, and modeling applications involving decay processes.