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, Mark and Andy, were hired for an assembly line. Mark could process 12 units per minute after one hour and 13 units per minute after two hours. Andy 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. Mark .................... Andy ....................

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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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, Mark and Andy, were hired for an assembly line. Mark could process 12 units per minute after one hour and 13 units per minute after two hours. Andy 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.

Mark ....................

Andy ....................

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