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

where \(k_{1}>0, k_{2}>0, A(t)\) 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.

1. Since the \(\mathrm{DE}\) is autonomous, use the phase portrait concept of Section $2.1$ to find the limiting value of \(A(t)\) as \(t \rightarrow \infty\). Interpret the result.
2. Solve the DE subject to \(A(0)=0\). Sketch the graph of \(A(t)\) and verify your prediction in part (a).

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