Part I On a certain university campus there is an infestation of Norway rats. It is...

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

A) It is estimated that there were 500 rats on campus on January 1, 2010 and 750 on April 1, 2010. Using this information, find an explicit formula for P(t)P(t) where tt is years since January 1, 2010. (Assume April 1, 2010 is t=.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 on April 1, 2010?
rats per year.

D) According to our logistic model, when will the rat population hit 2,500 rats?
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 is F=0.64P+4−−−−−−−−√−2F=0.64P+4−2 cubic meters when 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 to time?
The total volume is  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.

Solutions

Expert Solution

Colby Messinger answered 2 months ago

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