Two new workers were hired for an assembly line. Jim processed 25 units during the first hour and 45 units during the second hour. Mark processed 35 units during the first hour and 50 units the second hour. Using the model of Exercise 31 and assuming that $P(0)=0$, estimate the maximum number of units per hour that each worker is capable of processing.
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We are given that Jim processed 25 units in the first hour and 45 units in the second hour. Let $P_J(t)$ be the number of units processed by Jim at time $t$. Show more…
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Two new workers were hired for an assembly line. Jim processed 25 units during the first hour and 45 units during the second hour. Mark processed 35 units during the first hour and 50 units the second hour. Using the model of Exercise 31 and assuming that $P(0)=0$ , estimate the maximum number of units per hour that each worker is capable of processing.
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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, Sam and Joe, were hired for an assembly line. Sam could process 12 units per minute after one hour and 15 units per minute after two hours. Joe 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.
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