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Unformatted text preview: 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 ? dR dt = 100 t (40 + t ) (20 + t + t 2 ) 2 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...
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 Spring '08
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