Part I On a certain university campus there isan infestation of Norway rats. It is estimated that the number ofrats on campus will follow a logistic model of the formP(t)=50001+Be−ktP(t)=50001+Be−kt.

A) It is estimated that there were 500 rats oncampus on January 1, 2010 and 750 on April 1, 2010. Using thisinformation, find an explicit formula for P(t)P(t) where tt isyears since January 1, 2010. (Assume April 1, 2010 ist=.25t=.25.)
P(t)= P(t)=  .

B) What was the rat population on October 1,2010?
rats.

C) How fast was the rat population growing onApril 1, 2010?
rats per year.

D) According to our logistic model, when will therat population hit 2,500 rats?
years after January 1, 2010.

E) Rats live in communal nests and the more ratsthere are, the closer they live together. Suppose the total volumeof the rats' nests is F=0.64P+4−−−−−−−−√−2F=0.64P+4−2 cubic meterswhen there are PP rats 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 totime?
The total volume is  cubic meters and the volume isincreasing at  cubic meters per year.

F) One of the reasons that the rats' populationgrowth slows down is overcrowding. What is the population densityof the rats' nests when there are 750 rats and how fast is thepopulation density increasing at that time?
The population density is  rats per cubic meter and thepopulation density is increasing at  rats per cubic meterper year.