AP Calculus AB · Unit 7: Differential Equations
7.8 Exponential Models with Differential Equations
In short
You learn to set up and solve separable differential equations leading to models for exponential growth and decay. You must recognize the forms of differential equations resulting in exponential models (dy/dt = ky) and know that they have solutions of the form y = y0e^kt.
Last updated
What else do you need to know about Exponential Models with Differential Equations?
These models may be used or interpreted without performing the derivation.
How is Exponential Models with Differential Equations tested on the exam?
You need to practice setting up and solving contextual questions involving separable differential equations until the solution strategy becomes routine: separate variables, antidifferentiate both sides, add a constant of integration, use initial conditions to determine the constant, and rearrange to complete the solution. Failure to separate variables or omitting the constant of integration severely limits the number of points you can earn on the AP Exam. A common error is assuming that all differential equations involving fractions have logarithmic solutions. You must learn to recognize the forms of differential equations resulting in exponential models, which may be used or interpreted without performing the derivation. Differential equations give information about the derivative and may be used directly to find information about a slope or rate of change.
Free practice questions with full explanations, and instant marking of your free-response answers.
Exponential Models with Differential Equations: common questions
What do you need to know about Exponential Models with Differential Equations for AP Calculus AB?
You learn to set up and solve separable differential equations leading to models for exponential growth and decay. You must recognize the forms of differential equations resulting in exponential models (dy/dt = ky) and know that they have solutions of the form y = y0e^kt.
How is Exponential Models with Differential Equations tested on the AP Calculus AB exam?
You need to practice setting up and solving contextual questions involving separable differential equations until the solution strategy becomes routine: separate variables, antidifferentiate both sides, add a constant of integration, use initial conditions to determine the constant, and rearrange to complete the solution.
Where does Exponential Models with Differential Equations fit in AP Calculus AB?
Exponential Models with Differential Equations is topic 7.8 in Unit 7: Differential Equations of AP Calculus AB.
Want help mastering this topic?
Work through Exponential Models with Differential Equations one-on-one with an AP Guru tutor.
Book a free demo class