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c). Shrinks have discovered that there is a limit to the number of meaningless words that a person can learn, no matter how much study time is available, and that the rate of learning is proportional to the number of words not yet learnt. If this limit is 200 words, then the rate of learning satisfies the differential equation dw = k(200 – W) dt where k is a constant and W(t) is the number of words mastered in the first t minutes i). Explain why k is positive ii). Determine the solution to differential equation

c). Shrinks have discovered that there is a limit to the number of meaningless words that a person can learn, no matter how much study time is available, and that the rate of learning is proportional to the number of words not yet learnt. If this limit is 200 words, then the rate of learning satisfies the differential equation dw = k(200 – W) dt where k is a constant and W(t) is the number of words mastered in the first t minutes i). Explain why k is positive ii). Determine the solution to differential equation

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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c). Shrinks have discovered that there is a limit to the number of meaningless words that a person can learn, no matter how much study time is available, and that the rate of learning is proportional to the number of words not yet learnt. If this limit is 200 words, then the rate of learning satisfies the differential equation dw = k(200 – W) dt where k is a constant and W(t) is the number of words mastered in the first t minutes i). Explain why k is positive ii). Determine the solution to differential equation
Transcribed Image Text:c). Shrinks have discovered that there is a limit to the number of meaningless words that a person can learn, no matter how much study time is available, and that the rate of learning is proportional to the number of words not yet learnt. If this limit is 200 words, then the rate of learning satisfies the differential equation dw = k(200 – W) dt where k is a constant and W(t) is the number of words mastered in the first t minutes i). Explain why k is positive ii). Determine the solution to differential equation
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