Find the rate of new cases

Reference no: EM131798736

Question: Spread of disease 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, 1000 - x. 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.

Reference no: EM131798736

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