How to Solve K'(T) = k(M-K(t)) Using Given Values?

[chaotixmonjuish]

I'm not even sure how to start this question

K'(T)=k(M-K(t))
M=total knowledge

suppose that:
M=100
K(0)=0
and
K(2)=50

does this mean
k'(0)=k(100-0)
and
k'(2)=K(100-50)

 

[Defennder]

This looks like one of those ODE modeling questions. I think you have to elaborate more on what K, k, T and t are. More specifically tell us which variables the aforementioned functions are of. And K'(T) is dK/dt or dK/dT ?

 

[chaotixmonjuish]

K(t)is the total knowledge about how to perform at task at time t

K'(t) or the rate of change in K(t) is proportional to what we do not know yet or
K'(t)=k(M-K(t)) where M is total knowledge

it takes two years to learn 50% of the task, how long does it take to learn 75%

 

[Defennder]

Ok I take it that M is a constant and not a function of t and T and t are the same thing. k is also an unknown constant. So you have:

$$\frac{dK}{dt} = k(M-K)$$

So this is a 1st order ODE. It's clearly separable. Solve it for K(t) and plug in the given values of K(0) and K(2) to solve for the constant of integration and k.