Let P(t) be the performance level of someone learning a skill as a function of t

Question

Let P(t) be the performance level of someone learning a skill as a function of the training time t. The derivative 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 dP/dt = k(M - P(t)) where k is a positive constant. Two new workers, David and Peter, were hired for an assembly line. David could process 11 units per minute after one hour and 14 units per minute after two hours. Peter 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: Peter.

Explanation / Answer

david=15.125 peter=25

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