Question

Write first-order differential equations that express the situation: The increase in the number of people who have heard a rumor in a town of populati

First order differential equations
ANSWERED
asked 2021-07-05
Write first-order differential equations that express the situation: The increase in the number of people who have heard a rumor in a town of population 20,00020,000 is proportional to the product of the number PP who have heard the rumor and the number who have not heard the rumor at time tt .

Answers (1)

2021-07-06
\(\displaystyle{\frac{{{d}{P}}}{{{\left.{d}{t}\right.}}}}={k}{P}{\left({20},{000}-{P}\right)},{\left({k}{>}{0}\right)}\)
P is the number of people who have heard the rumor and 20,000-P is the number of people who have not heard the rumor. k is the proportionality constant.
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