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(3 points) Part I On a certain university campus there is an infestation of Norway rats It is estimated that the number of rats on campus wi follow a logistic model of the torm P) A) Iit is estimated that there were 500 rats on campus on January 1, 2010 and 750 on Apria 1, 2010 Using this information, find an explicit formula for P0) where t is years since January 1,2010 (Assume Apnil 1,2010 s25 P(t) 5000/1+9eY-1.85) B) What was the rat population on October 1, 2010 1540 rats C) How tast was the rat population growing on April 1,2010 1179 28 rats per year D) According to our logistic model ywhen will the rat population hit 2,500 rats? 1.187 years after January 1, 2010 E) Rats live in communal nests and the more rats there are, the closer they live together Suppose the total volume of the rats nests s F = v/064PT-4-2 cubic meters when there are Frats on campus When there are 750 rats, what is the total volume of the rats' nests and how fast is the mass of nests growing with respect to time? The total volume is 20 cubic meters and the volume is increasing at cubic meters per year F) One of the reasons that the rats' population growth slows down is overcrowding What is the population density of the rats' nests when there are 750 rats and how fast is the population density increasing at that time? The population density is rats per cubic meter and the population density is increasing at rats per cubic meter per year