7.8 Exponential Models with Differential Equations
- Syllabus
- 2020
- Topic
- 7.8
- Level
- —
Learning objectives
—FUN-7.F—Interpret the meaning of a differential equation and its variables in context• FUN-7.F Interpret the meaning of a differential equation and its variables in context.• FUN-7.F.1 Specific applications of finding general and particular solutions to differential equations include motion along a line and exponential growth and decay.• FUN-7.F.2 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.• Enduring understanding FUN-7: Solving differential equations allows us to determine functions and develop models.—FUN-7.G—Determine general and particular solutions for problems involving differential equations in context• FUN-7.G Determine general and particular solutions for problems involving differential equations in context.• FUN-7.G.1 The exponential growth and decay model, dy/dt = ky, with initial condition y = y₀ when t = 0, has solutions of the form y = y₀eᵏᵗ.• Enduring understanding FUN-7: Solving differential equations allows us to determine functions and develop models.
FUN-7.F—Interpret the meaning of a differential equation and its variables in context
- FUN-7.F Interpret the meaning of a differential equation and its variables in context.
- FUN-7.F.1 Specific applications of finding general and particular solutions to differential equations include motion along a line and exponential growth and decay.
- FUN-7.F.2 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.
- Enduring understanding FUN-7: Solving differential equations allows us to determine functions and develop models.
FUN-7.G—Determine general and particular solutions for problems involving differential equations in context
- FUN-7.G Determine general and particular solutions for problems involving differential equations in context.
- FUN-7.G.1 The exponential growth and decay model, dy/dt = ky, with initial condition y = y₀ when t = 0, has solutions of the form y = y₀eᵏᵗ.
- Enduring understanding FUN-7: Solving differential equations allows us to determine functions and develop models.