Let P(t)P(t) be the performance level of someone learning a skill as a function of the training time tt. The derivative dPdtdPdt represents the rate at which performance improves. If MM is the maximum level of performance of which the learner is capable, then a model for learning is given by the differential equation

dPdt=k(M−P(t))dPdt=k(M−P(t))

where kk is a positive constant.
Two new workers, Andy and Peter, were hired for an assembly line. Andy could process 1212 units per minute after one hour and 1313 units per minute after two hours. Peter could process 1111 units per minute after one hour and 1414 units per minute after two hours. Using the above model and assuming that P(0)=0P(0)=0, estimate the maximum number of units per minute that each worker is capable of processing.
Andy: ,