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# P14 - Project 14 MAC 2311 YOU MUST SHOW YOUR WORK TO...

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Project 14 MAC 2311 YOU MUST SHOW YOUR WORK TO RECEIVE FULL CREDIT!! 1. A sociologist determines that the percentage of our MAC 2311 class that has heard a rumor about the next exam 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 in this context? Calculate dR dt , simplify, and factor if possible. What is the rate of change of R ( t ) with respect to t at present? Include units. What percentage of the class 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 with your answers—round to the nearest tenth.) 1

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How many days does it take for forty percent of the class to hear the rumor? What is the rate of change of R ( t ) with respect to t at this time? (Include units with your answer.) How many days does it take for fifty percent of the class to hear the rumor?
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