An epidemic spreads through a population at a rate proportional to the product of the number of people already infected and the number of people susceptible, but not yet infected. Therefore, if S denotes the total population of susceptible people and I I(t) denotes the number of infected people at time t, then = I'= rI(S-I), where r is a positive constant. A) Let's say that there are 2000 susceptible people in a nursing home, so S = 2000. Let's also say that one infected person visits the home, so that I(0) = 1. Find the function I(t) for the number of peope infected at time t > 0. I(t) = B) If the infection rate is r = 0.0004, how many people are infected after t = 5 days? (Whole people only, please) C) As the value of t increases, can you see what I(t) become? In other words, calculate the following limit lim I(t) = t→∞

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