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In the 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. Assume that the rate at which material is forgotten is proportional to the amount memorized. Suppose M denotes the total amount of a subject to be memorized and A(1) is the amount memorized in time >0. Determine a differential equation for the amount A(1) when forgetfulness is taken into account. (Assume the constants of proportionality for the rate at which material is memorized and the rate at which material is forgotten are k, >0 and k₂ > 0, respectively. Use A for A(1).)

In the 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. Assume that the rate at which material is forgotten is proportional to the amount memorized. Suppose M denotes the total amount of a subject to be memorized and A(1) is the amount memorized in time >0. Determine a differential equation for the amount A(1) when forgetfulness is taken into account. (Assume the constants of proportionality for the rate at which material is memorized and the rate at which material is forgotten are k, >0 and k₂ > 0, respectively. Use A for A(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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5. In the 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. Assume that the rate at which material is forgotten is proportional to the amount memorized. Suppose M denotes the total amount of a subject to be memorized and A(1) is the amount memorized in timet > 0. Determine a differential equation for the amount A(1) when forgetfulness is taken into account. (Assume the constants of proportionality for the rate at which material is memorized and the rate at which material is forgotten are k, > 0 and k₂ > 0, respectively. Use A for A (1).)
Transcribed Image Text:5. In the 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. Assume that the rate at which material is forgotten is proportional to the amount memorized. Suppose M denotes the total amount of a subject to be memorized and A(1) is the amount memorized in timet > 0. Determine a differential equation for the amount A(1) when forgetfulness is taken into account. (Assume the constants of proportionality for the rate at which material is memorized and the rate at which material is forgotten are k, > 0 and k₂ > 0, respectively. Use A for A (1).)
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