As you know, when a course ends, 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).