Capacitor Discharging: Exponential Decay Graphs and Tangent Interpretation

This example demonstrates the discharging process of a capacitor by modeling how charge or voltage decays over time and visualizing it as an exponential decay curve. It highlights key mathematical ideas: exponential functions, function graphing, and the geometric meaning of a tangent line (local rate/change captured by the tangent). The construction uses GeoGebra’s geometry tools—especially the command “Segment”—to build essential elements such as time-parameter positions and connecting segments, along with labeled objects (e.g., E, t, Γ, a, A, M, f, B, C, b, D, g, h, i, and multiple text labels) to annotate the graph and indicate relevant points/lines. Interactive controls (button objects) support step-by-step exploration of the curve and its tangent interpretation. Suitable for upper-secondary students through early university learners, particularly for teaching exponential models, graph interpretation, and an intuitive introduction to calculus concepts via tangents.