When forgetfulness is taken into account, the rate of memorization of a subject is given by (d A)/(d t)=k1(M-A)-k2 A where k1>0, k2>0, A(t) is the amount memorized in time t M is the total amount to be memorized, and M-A is the amount remaining to be memorized. (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 →∞Interpret the result. (b) Solve the DE subject to A(0)=0 . Sketch the graph of A(t) and verify your prediction in part
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