# P12 - Project 12 MAC 2311 1 A sociologist determines that...

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Project 12 MAC 2311 1. A sociologist determines that the percentage of a population that has heard a rumor t days after the rumor begins to circulate ( t = 0 ) is given by R ( t ) = 100 t 2 20 + t + t 2 What is the domain of R ( t ) in this context? Calculate R (0) and lim t →∞ R ( t ) . Do your answers make sense? Calculate dR dt , simplify, and factor. Does the derivative ever change sign for t 0 ? What is the initial rate of change of R ( t ) with respect to t ? (Include units.) How can this be? What percentage of the population has heard the rumor after one day? What is the rate of change of R ( t ) with respect to t at that time? (Include units; round to the nearest tenth.) How many days pass before forty percent of the population has heard the rumor? ﬁfty per- cent? What is the rate of change of R ( t ) with respect to t at those time? (Include units.) Of the times examined above, what was the general trend (up and down) of the rate at which the rumor is spread? Brieﬂy explain why you think this might be true about the spread of a rumor.

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2. A population (in thousands) of black bears in a national park is represented by the function
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P12 - Project 12 MAC 2311 1 A sociologist determines that...

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