# . Spread of a Disease The rate r at which a disease spreadsin a population of size P is jointly proportional to the number xof infected people and the number P  x who are not infected.An infection erupts in a small town that has populationP  5000.(a) Write an equation that expresses r as a function of x.(b) Compare the rate of spread of this infection when10 people are infected to the rate of spread when1000 people are infected. Which rate is larger? Bywhat factor?(c) Calculate the rate of spread when the entire population isinfected. Why does this answer make intuitive sense?

Question

. Spread of a Disease 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 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?