The spread of a rumor through a small town is modeled by

Chapter 6, Problem 67

(choose chapter or problem)

The spread of a rumor through a small town is modeled by dy/dt ! 1.2y(1 " y), where y is the proportion of the townspeople who have heard the rumor at time t in days. At time t ! 0, ten percent of the townspeople have heard the rumor. (a) What proportion of the townspeople have heard the rumor when it is spreading the fastest? 1/2 (b) Find y explicitly as a function of t. (c) At what time t is the rumor spreading the fastest?

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