Spread of a Disease The rate r at which a disease spreads in a population of size P is jointly proportional to the number.r of infected people and the number P - x who are not infected. An infection erupts in a small town that has population P = 5000. (a) Write an equation that expresses r as a function of x. (b) Compare the rate of spread of this infection when 10 people are infected to the rate of spread when 1000 people are infected. Which rate is larger? By what factor? (c) Calculate the rate of spread when the entire population is infected. Why does this answer make intuitive sense?

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