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In a theory of learning, the rate at which a subject is memorized is assumed to be proportional to the amount that is left to be memorized. Suppose M denotes the amount of a subject to be memorized and y(t) is the amount memorized in time t. Determine and solve a differential equation for the amount y(t). Assume y(0) = 1

In a theory of learning, the rate at which a subject is memorized is assumed to be proportional to the amount that is left to be memorized. Suppose M denotes the amount of a subject to be memorized and y(t) is the amount memorized in time t. Determine and solve a differential equation for the amount y(t). Assume y(0) = 1

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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In a theory of learning, the rate at which a subject is memorized is assumed to be proportional to the amount that is left to be memorized. Suppose \( M \) denotes the amount of a subject to be memorized and \( y(t) \) is the amount memorized in time \( t \). Determine and solve a differential equation for the amount \( y(t) \). Assume \( y(0) = 1 \).
Transcribed Image Text:In a theory of learning, the rate at which a subject is memorized is assumed to be proportional to the amount that is left to be memorized. Suppose \( M \) denotes the amount of a subject to be memorized and \( y(t) \) is the amount memorized in time \( t \). Determine and solve a differential equation for the amount \( y(t) \). Assume \( y(0) = 1 \).
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