Question

in the theory of learning the rate at which the subject is memorized is assumed to be directly proportional to the amount left to be memorized. also the rate at which the subject is forgotten is directly proportional to the amount memorized in their time t. suppose M denotes the total amount to be memorized and A(t) is the amount memorized at any time t. Determine the differential equation of A(t)

Answer 1

dA/dt = k(M-A) - cA

dA/dt = k M - kA - c A

but k - c is a constant call it r

dA/dt = kM- rA

dA/dt +rA = k M = constant for this case of M