Writing Equations for Exponential Functions Using Geometric Mean

This GeoGebra lesson demonstrates how to derive and write equations for exponential functions from geometric relationships built with segments and proportions. It highlights the exponential model by using the geometric mean idea to connect intermediate quantities with endpoints, clarifying how growth/decay behavior corresponds to a specific functional form. Key math concepts include writing exponential function equations, geometric mean (Geometric Mean), division/proportional reasoning using line segments, and organizing the construction with labeled points and staged visuals. Construction-wise, it uses multiple interactive buttons (button1–button6) and a state controller to step through the workflow; points A–H serve as the anchor locations for segment and proportion setup; several text objects (text1–text6, text4–text6) label parameters and intermediate values; and pic1/pic2 present different diagram stages for guided understanding. Suitable for middle school advanced algebra through high school, especially for instruction on exponential functions, equation formation, and visual modeling.