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At a time denoted as t= 0 a technological innovation is introduced into a community that has a fixed population of n people. Determine a differential equation for the number of people x(t) who have adopted the innovation at time t if it is assumed that the rate at which the innovations spread through the community is jointly proportional to the number of people who have adopted it and the number of people who have not adopted it. (Use k> 0 for the constant of proportionality and x for x(t). Assume that initially one person adopts the Innovation.) kxn-x x(0) - Need Help? Road I

At a time denoted as t= 0 a technological innovation is introduced into a community that has a fixed population of n people. Determine a differential equation for the number of people x(t) who have adopted the innovation at time t if it is assumed that the rate at which the innovations spread through the community is jointly proportional to the number of people who have adopted it and the number of people who have not adopted it. (Use k> 0 for the constant of proportionality and x for x(t). Assume that initially one person adopts the Innovation.) kxn-x x(0) - Need Help? Road I

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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At a time denoted as t= 0 a technological innovation is introduced into a community that has a fixed population of n people. Determine a differential equation for the number of people x(t) who have adopted the innovation at time t if it is assumed that the rate at which the innovations spread through the community is jointly proportional to the number of people who have adopted it and the number of people who have not adopted it. (Use k> 0 for the constant of proportionality and x for x(t). Assume that initially one person adopts the innovation.) dxkx n-X dt x(0) = Need Help? Read It
Transcribed Image Text:At a time denoted as t= 0 a technological innovation is introduced into a community that has a fixed population of n people. Determine a differential equation for the number of people x(t) who have adopted the innovation at time t if it is assumed that the rate at which the innovations spread through the community is jointly proportional to the number of people who have adopted it and the number of people who have not adopted it. (Use k> 0 for the constant of proportionality and x for x(t). Assume that initially one person adopts the innovation.) dxkx n-X dt x(0) = Need Help? Read It
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