a) Assume that the rate at which you can memorize a subject is proportional to t

Question

a) Assume that the rate at which you can memorize a subject is proportional to the amount that is left to be memorized. If M denotes the total amount of the subject, and A(t) is the amount memorized in time, determine the differential model for A(t) Denote the proportional factor as alpha.

b) Now add forgetting. Assume that the rate at which the material is forgotten is proportional to the amount memorized in time t, that is, beta*A(t). Determine the differential model for the combination of memorizing(in part a) and forgetting at the same time.

Explanation / Answer

M = total amount of a subject.

A(t) = amount memorized by time, t

M-A(t) = amount left to memorize --> this is proportional to memorization rate

A'(t) = alpha*(M-A)

Forgetting = beta*A

A'(t) = memorizing - forgetting

A'(t) = alpha(M-A) - beta*A

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