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how do i write the differential equation of a learning curve?

i need to write the differential equation of the learning curve which is the quantity that grows at a rat that is proportional to the difference between its size and a fixed upper bound. HELP!

Public Comments

1. generally the change is proportional to the product of amount learned and amount to yet learn x= learned , Q = total quantity to learn dx/dt = k x [ Q-x] , x(0) = 0
2. Just like the problem says (BTW, get rid of the rat....) Call the learning function L(x), its upper bound Lup, k the proportionality constant then dL/dx = k[Lup-L(x)] Read it: the rate, dL/dx, is proportional,k, to the difference between its size and a fixed upper bound, Lup - L(x).