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dx = k(a- x)x dt

dx = k(a- x)x dt

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Hello! Need some help with these problem regarding applications of calculus

6. A variation on the population problem is when the population size has an inhibitory effect on the growth of the population. Hence, if x is the population size, then dx k(a- x)x %3D dt This kind of model can be extended to many situations, called self-limiting problems. One person in a small town with a population of 200 proceeds to spread a rumor. If the rate at which the rumor spreads is proportional to the number of people who know the rumor (x) as well as the number of people who do not know, find an expression for the number of people who know about the rumor after t days. Fifty people know about the rumor after one day. How many people will have heard of the rumor after 2 days? Will the entire town eventually hear the rumor? Ans. 191
Transcribed Image Text:6. A variation on the population problem is when the population size has an inhibitory effect on the growth of the population. Hence, if x is the population size, then dx k(a- x)x %3D dt This kind of model can be extended to many situations, called self-limiting problems. One person in a small town with a population of 200 proceeds to spread a rumor. If the rate at which the rumor spreads is proportional to the number of people who know the rumor (x) as well as the number of people who do not know, find an expression for the number of people who know about the rumor after t days. Fifty people know about the rumor after one day. How many people will have heard of the rumor after 2 days? Will the entire town eventually hear the rumor? Ans. 191
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