Logistic Growth Model with Slope Field (Differential Equation Visualization)

① This GeoGebra example dynamically demonstrates the logistic growth model, a first-order differential equation, together with its slope field, visually showing the S-shaped growth curve under a finite carrying capacity. ② Core mathematical concepts include ordinary differential equations, logistic equation, equilibrium solutions, inflection point (buigpunt), slope fields, and how parameters affect solution curves. ③ Construction highlights: uses GeoGebra commands such as SlopeField to generate the direction field, Intersect for finding intersections, OrthogonalLine for perpendicular lines, and Segment for line segments; key objects include parameters k (growth rate), M (carrying capacity), P0 (initial value), solution function f, second derivative f'', and the inflection point, with sliders (aantal, a, b) for dynamic parameter adjustment. ④ Suitable for senior high school or early university students learning differential equations, useful for understanding logistic growth and slope fields, and applicable in mathematical biology or ecology modeling.