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University of North Texas

# A model for the spread of a rumor is given by the equation$$p(t) = \dfrac{1}{1 + ae^{-kt}}$$where $p(t)$ is the proportion of the population that knows the rumor at the time $t$ and $a$ and $k$ are positive constants.(a) When will half the population have heard the rumor?(b) When is the rate of spread of the rumor greatest?(c) Sketch the graph of $p$.

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University of North Texas

Derivatives

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