differential equation world problems

A learning curve is the graph of a function P(t), the performance of someone learning a skill as a function of 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 t increases? Explain.

b) If M is the maximum level of performance of which the learner is capable, explain why the differential equation dP / dt = k(M-P), k a positive constant is a reasonable model for learning.

a) answer is that it increases most rapidly in the beginning then begins to decline. can anyone tell me why this is so?

b)?