Question: As you know, when a course ends, the students start to forget the material they have learned. One model (called the Ebbinghaus model) assumes that the rate at which a student forgets material is proportional to the difference between the material currently remembered and some positive constant, \(a\).

a.) Let \(y=f(t)\) be the fraction of the original material remembered \(t\) weeks after the course has ended. Set up a differential equation for y. Your equation will

contain two constants; the constant a is less than \(y\) for all \(t\).

b. Solve the differential equation.

c.) Describe the practical meaning (in terms of the amount remembered) of the constants in the solution \(y=f(t)\).

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