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Question

The rate r at which a disease spreads in a population of size P is jointly proportional to the number x of infected people and the number P − x

 who are not infected. An infection erupts in a small town with population P = 6,000.

(a)

Write an equation that expresses r as a function of x. (Use k for the constant of proportionality and P for the population.)

Answer 1

r = kx(P - x)

Since P = 6000, r = kx(6000 - x), where k is a constant.