In the theory of learning the rate at which a subject is mem

In the theory of learning, the rate at which a subject is memorized is assumed to be proportional to the amount that is left to be memorized. Assume that the rate at which material is forgotten is proportional to the amount memorized. Suppose M denotes the total amount of a subject to be memorized and A(t) is the amount memorized in time t > 0. Determine a differential equation for the amount A(t) when forgetfulness is taken into account. (Assume the constants of proportionality for the rate at which material is memorized and the rate at which material is forgotten are k_1 > 0 and k_2 > 0, respectively. Use A for A(t).)

Solution

ANSWER :-

The differential equation A(t) is given by

dA/dt = k₁(M-A) - k₂A

Here we assume the constants of proportionality for the rate at which the material is memorized and at the rate which material is forgotten are k₁>0 and k₂>0.