2-28 - learning Problem 33 9.1 Psychologists inter-ested...

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February 28, 2005 Announcements: Reading from the book: § 9.1, § 9.3 and § 9.4. The last 2 homeworks will not be collected. Last quiz of the quarter, Tuesday March 1, 2005 Problems 1, 5, 7, 11, 12, and 15 from section 8.3 are not part of this week’s assignment. Midterm solutions can be found in ; toro/Courses/04- 05/highlights.html Today § 9.1 Modeling with differential equations.
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Problem 13, § 9.1: Psychologists inter- ested in learning theory study learning curves . A learning curve is the graph of a function P ( t ), the performance of someone learning a skill as a function of the training time t . The derivative dP/dt represents the rate at which performance improves. 1. When do you think P increases most rapidly? What happens to dP/dt as t increases? 2. If M is the maximum level of perfor- mance of which the learner is capable, what would be a reasonable model for
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Unformatted text preview: learning? Problem 33, § 9.1: Psychologists inter-ested in learning theory study learning curves . A learning curve is the graph of a function P ( t ), the performance of someone learning a skill as a function of the training time t . The learning process is modeled by the dif-ferential equation dP dt = k ( M-P ) , where M is the maximum level of perfor-mance, and k is a positive constant. Solve this differential equation to find an expres-sion for P ( t ). What is the limit of this ex-pression? Problem 3, § 9.1: 1. For what non-zero values of k does the function y = sin kt satisfy the differen-tial equation y 00 + 9 y = 0. 2. For those values of k , verify that every member of the family of functions y = A sin kt + B cos kt is also a solution....
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