Memorization When forgetfulness is taken into account, the rate of memorization of a...

Memorization When forgetfulness is taken into account, the rate of memorization of a subject is given by

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 Interpret the result.

(b) Solve the DE subject to A(0) = 0. Sketch the graph of A(t) and verify your prediction in part (a).