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Exponential Models

Analyzing exponential models with differential equations.

Mapped to AP College Board # FUN-7, FUN-7.F, FUN-7.F.1, FUN-7.F.2, FUN-7.G, FUN-7.G.1

Solving differential equations allows us to determine functions and develop models. Interpret the meaning of a differential equation and its variables in context. Specific applications of finding general and particular solutions to differential equations include motion along a line and exponential growth and decay. The model for exponential growth and decay that arises from the statement “The rate of change of a quantity is proportional to the size of the quantity” is dy/dt = ky. Determine general and particular solutions for problems involving differential equations in context. The exponential growth and decay model, dy/dt = ky with initial condition y = y0 when t = 0, has solutions of the form y= y0 e^(kt).