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University of North Texas

Psychologists interested 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.(a) When do you think $P$ increases most rapidly? What happens to $dP/dt$ as $t$ increase? Explain.(b) If $M$ is the maximum level of performance of which the learner is capable, explain why the differential equation $\frac {dP}{dt} = k(M - P)$ $K$ a positive constant

(a) $P$ increases most rapidly at the beginning, since there are usually many simple, easily-learned sub-skills associated with learning a skill. As $t$ increases, we would expect $d P / d t$ to remain positive, but decrease. This is because as time progresses, the only points left to learn are the more difficult ones.(b) $\frac{d P}{d t}=k(M-P)$ is always positive, so the level of performance $P$ is increasing.As $P$ gets close to $M, \frac{d P}{d t}$ gets close to $0 ;$ that is, the performance levels off, as explained in part (a)(c) See graph

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Campbell University

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Baylor University

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Idaho State University

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University of North Texas

Topics

Differential Equations

Anna Marie V.

Campbell University

Caleb E.

Baylor University

Samuel H.

University of Nottingham

Michael J.

Idaho State University

Lectures

Join Bootcamp