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. Suppose M denotes the total amount of a subject to be memorized and A(t) is the amount memorized in time t. Determine a differential equation for the amount A(t). Now assume that the rate at which material is forgotten is proportional to the amount memorized in time t. Determine a differential equation for the amount A(t) when forgetfulness is taken into account.
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. Suppose M denotes the total amount of a subject to be memorized and A(t) is the amount memorized in time t. Determine a differential equation for the amount A(t). Now assume that the rate at which material is forgotten is proportional to the amount memorized in time t. Determine a differential equation for the amount A(t) when forgetfulness is taken into account.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 13EQ
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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. Suppose M denotes the total amount of a subject to be memorized and A(t) is the amount memorized in time t. Determine a differential equation for the amount A(t). Now assume that the rate at which material is forgotten is proportional to the amount memorized in time t. Determine a differential equation for the amount A(t) when forgetfulness is taken into account.
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