AP Calculus BC 7.9 Logistic Models with Differential Equations Concept

FUN-7.H Interpret the meaning of the logistic growth model in context.
FUN-7.H.1 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).
FUN-7.H.2 The logistic differential equation and initial conditions can be interpreted without solving the differential equation.
FUN-7.H.3 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.
FUN-7.H.4 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.
Enduring understanding FUN-7: Solving differential equations allows us to determine functions and develop models.

7.9 Logistic Models with Differential Equations