Practice with Exponential Functions of Base e: Graphs and Properties

This example demonstrates how exponential functions with base e behave under different parameter choices, focusing on the resulting graph shapes and qualitative changes. Key concepts include the natural exponential model y = a·e^(bx), exponential growth vs. decay, monotonicity, and the presence of a horizontal asymptote implied by the exponential form. The construction is centered on defining an exponential function in GeoGebra and graphing it in the same coordinate plane for comparison across parameter sets. Typically, it relies on GeoGebra’s function-graph features to create the function object f(x) = a*e^(b*x) and visualize its curve. If the practice is interactive, sliders (slider) are used to dynamically control parameters a and b, enabling students to observe how the curve’s direction (increasing/decreasing) and key features (e.g., asymptotic behavior) change in real time. Suitable for late secondary through introductory college coursework, including function analysis and pre-calculus or early calculus preparation.