In: Math
a virus is spreading on a small deserted island. The total number of people infected by the virus t days after the outbreak is given 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 250 patients. When will the total number of infections reach 250?
c. After how many days does the rate of new infections reach a maximum? Justify your answer carefully using calculus. Approximately how many people will be newly infected on that day?