An isolated community of 1000 people susceptible to a certain disease is exposed when one member returns carrying the disease. If x represents the number infected with the disease at time t (in days), then the rate of change of x is proportional to the product of the number infected, x, and the number still susceptible, 1000x. That is, dx/dt =kx (1000-x) or dx/x(1000-x)=k dt

(a) If k=0.001, integrate both sides to solve this differential equation.

(b) Find how long it will be before half the population of the community is affected.

(c) Find the rate of new cases, dx/dt, every other day for the first 13 days.