Memorization When forgetfulness is taken into account, the rate of memorization of a
Chapter 2, Problem 42(choose chapter or problem)
Memorization When forgetfulness is taken into account, the rate of memorization of a subject is given by dA dt = k1(M - A) - ki,A, where k1 > 0, k2 > 0, A(t) is the amount to be memorized in time t, Mis the total amount to be memorized, and M - A is the amount remaining to be memorized. See 25 and 26 in Exercises 1.3. (a) Since the DE is autonomous, use the phase portrait concept of Section 2.1 to find the limiting value of A(t) as t oo. Interpret the result. (b) Solve for A(t) subject to A(O) = 0. Sketch the graph of A(t) and verify your prediction in part (a).
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