Psychologists interested in learning theory study learning curves. A learning curve is the graph of a function, the performance of someone learning a skill as a function of the training time t. The derivative dP/dt represents the rate at which performance improves.
(a) When do you think P increases most rapidly? What happens to dP/dt as increases? Explain.
(b) If is the maximum level of performance of which the learner is capable, explain why the differential equation
dP/dt = k(M - P)
is a reasonable model for learning.