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.) 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(r) who have adopted the innovation at time t if it is assumed that the rate at which the innovations spread through the community is jointlyproportional 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.)x(0) =

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Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

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.)