A community of 1,000 people is homogeneously mixed. One person who has just returned from another community has influenza. Assume that the home community has not had influenza shots and all are susceptible. One mathematical model assumes that influenza tends to spread at a rate in direct proportion to the number N who have the disease and to the number 1,000 - N who have not yet contracted the disease. Mathematically,

where N is the number of people who have contracted influenza after t days. For k = 0.0004, N(t) is given by

(A) How many people have contracted influenza after 10 days? After 20 days?
(B) How many days will it take until half the community has contracted influenza?
(C) Find limt †’ ˆž N(t).
(D) Graph N = N{t) for 0 ‰¤ t ‰¤ 30.

Transcribed Image Text:

dN -= kN(1,000-N) dt N(0) = 1 -1990 1,000 N(t) 1 +999e 0.4