In a model of how influenza spreads let nt denote the

Question

Question: In a model of how influenza spreads, let N(t) denote the number of persons who develop influenza t days after all members of a group of 1000 people have been in contact with a carrier of infection. Assume that

N^.(t) = 0.39N(t)(1 - N(t)/1000).          N(0) = 1

(a) Find a formula for N(t). How many develop influenza after 20 days?

(b) How many days does it take until 800 are sick?

(c) Will all 1000 people eventually get influenza?