Parametric Exponential Decay Family f(x)=a(1-e^(-bx))+c

This GeoGebra example dynamically explores the family of exponential decay functions defined by f(x)=a(1-e^(-bx))+c, where parameters a, b, and c control the vertical scaling, decay rate, and vertical shift respectively. The core mathematical concepts include exponential functions, function transformations (translation and scaling), and the effect of parameters on the graph's shape and position. The construction uses Textfield objects to create input boxes (InputBox1, InputBox2, InputBox3) for adjusting a, b, and c, along with the function f for plotting. Additional objects such as g, h, d, text2, e, i, text3, text5, j, k, and text4 are included for labeling or auxiliary analysis. This resource is suitable for high school or early college students to understand exponential decay models, parameter sensitivity, and to support discussions on asymptotes and rates of change in calculus.