Analyzing logistic models with differential equations.
Mapped to AP College Board # FUN-7, FUN-7.H, FUN-7.H.1, FUN-7.H.2, FUN-7.H.3, FUN-7.H.4
Solving differential equations allows us to determine functions and develop models. Interpret the meaning of the logistic growth model in context. The model for logistic growth that arises from the statement “The rate of change of a quantity is jointly proportional to the size of the quantity and the difference between the quantity and the carrying capacity” is dy/dt = ky(a-y). The logistic differential equation and initial conditions can be interpreted without solving the differential equation. The limiting value (carrying capacity) of a logistic differential equation as the independent variable approaches infinity can be determined using the logistic growth model and initial conditions. The value of the dependent variable in a logistic differential equation at the point when it is changing fastest can be determined using the logistic growth model and initial conditions.