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, John and Bob, were hired for an assembly line. John could process 11 units per minute after one hour and 13 units per minute after two hours.
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Bob 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.
I don't know what type of differential equation this is. So far in class we've only covered, linear, separable, and substitution methods for solving these.