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 = 4000.

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

(b) Compare the rate of spread of this infection when 70 people are infected to the rate of spread when 700 people are infected. Which rate is larger? By what factor? (Round your answer to one decimal place.)
The infection rate when 700 people are i

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 = 4000.


(a) Write an equation that expresses r as a function of x. (Use k for the constant of proportionality.)
r =	



(b) Compare the rate of spread of this infection when 70 people are infected to the rate of spread when 700 people are infected. Which rate is larger? By what factor? (Round your answer to one decimal place.)
The infection rate when 700 people are i