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.** Let

be the fraction of the original material remembered

weeks after the course has ended. Set up a differential equation for

, using

as any constant of proportionality you may need (let

). Your equation will contain two constants; the constant

(also positive) is less than

for all

.

What is the initial condition for your equation?

**B.** Solve the differential equation.

**C.** What are the practical meaning (in terms of the amount remembered) of the constants in the solution

? If after one week the student remembers 80 percent of the material learned in the semester, and after two weeks remembers 69 percent, how much will she or he remember after summer vacation (about 14 weeks)?

percent = _______________

^ I solved everything else just need to know C) Thank you!!