As an epidemic spreads through a population, the rate at which people are infected is often proportional to the product of the number of people infected and the number of people who are not infected.
a) If C denotes the total population, P denotes the number of infected people, and P0 denotes the initial number of infected people, write down an initial value problem modeling such an epidemic.
b) Solve the initial value problem in part (a).
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