\(\displaystyle{\frac{{{d}{P}}}{{{\left.{d}{t}\right.}}}}={k}{P}{\left({20},{000}-{P}\right)},{\left({k}{>}{0}\right)}\)

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.

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.