Let be the performance level of someone learning a skill as a function of the training time . 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, John and Bob, were hired for

an assembly line. John could process 12 units per minute after one hour and 14 units per minute after two hours. Bob could process 10 units per minute after one hour and 15 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.