A learning cuvre is the graph of a function P(t) that represents the performance level of someone who has trained at a skill for t hours. dP/dt represents the rate at which the performance level improves. If M (a positive constant is the maximum performance level of which the learner is capable, then which differential equations could be a reasonable model for learning?

Question

I. dP/dt = k(M-P)
II. dP/dt = k(P)
lll. dP/dt = k(M-P)^(1/2)
IV. dP/dt=k/(M-P)
** k = some positive constant

Answer 1

I've done a couple of these. This is very similar.
Why don't you give it a try, and show what you get?

Answer 2

The first one seems reasonable.
The second one goes up forever
The third one' s derivative goes crazy as P--->M
The fourth one is just silly