Let $P(t)$ be the performance level of someone learning a skill as a function of the training time $t$. The derivative $\displaystyle \frac{dP}{dt}$ represents the rate at which performance improves. If $M$ is the maximum level of performance of which the learner is capable, then a model for learning is given by the differential equation $$\frac{dP}{dt} = k(M-P(t))$$ where $k$ is a positive constant.
Two new workers, David and John, were hired for an assembly line. David could process $11$ units per minute after one hour and $15$ units per minute after two hours. John could process $10$ units per minute after one hour and $16$ units per minute after two hours. Using the above model and assuming that $P(0)=0$, estimate the maximum number of units per minute that each worker is capable of processing.
David: ,
John: .