Learning curves are studied by psychologists interested in the theory of learning. A learning curve is the graph of a function PL(t) that represents the performance dPL level of someone who has trained at a skill for thours. Thus, the dt represents the rate at which the performance level improves. By convention, the derivative PL(t) is taken to be a positive function. If M (a positive constant) is the maximum performance level of which the learner is capable, then which differential equations could be a reasonable model for learning (or more precisely, performance level)? Use your common sense applied to the practical meaning behind each equation to determine which of the following are reasonable. I. II. dP L k(M-PL) dt IV. dPL = k (PL) dt dP L = III. dt dPL at for some positive constant k for some positive constant k =k(M-P₁) ¹/2 I only I and II only III only I and III only IV only for some positive constant k k (M-PI) for some positive constant k

Learning curves are studied by psychologists interested in the theory of learning. A learning curve is the graph of a function PL(t) that represents the performance dPL level of someone who has trained at a skill for thours. Thus, the dt represents the rate at which the performance level improves. By convention, the derivative PL(t) is taken to be a positive function. If M (a positive constant) is the maximum performance level of which the learner is capable, then which differential equations could be a reasonable model for learning (or more precisely, performance level)? Use your common sense applied to the practical meaning behind each equation to determine which of the following are reasonable. I. II. dP L k(M-PL) dt IV. dPL = k (PL) dt dP L = III. dt dPL at for some positive constant k for some positive constant k =k(M-P₁) ¹/2 I only I and II only III only I and III only IV only for some positive constant k k (M-PI) for some positive constant k

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter5: A Survey Of Other Common Functions

Section5.4: Combining And Decomposing Functions

Problem 14E: Decay of Litter Litter such as leaves falls to the forest floor, where the action of insects and...

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