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a virus is spreading on a small deserted island. The total number of people infected by...

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Basic Math

a virus is spreading on a small deserted island. The totalnumber of people infected by the virus t days after the outbreak isgiven by the model p(t)=5200/(1+20^(-t+15)).

the different parts can be solved independently.

a. How many people will be infected in the long run? (hint:compute the limit of p as t goes too infinity.)

b. The island only has a small hospital with a capacity of 250patients. When will the total number of infections reach 250?

c. After how many days does the rate of new infections reach amaximum? Justify your answer carefully using calculus.Approximately how many people will be newly infected on thatday?

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