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. Compare the rate of spread of this infection when 90 people are infected to the rate of spread when 1400 people are infected. Which rate is larger? By what factor? (Round your answer to one decimal place.)
1. The infection rate when 1400 people are infected is about _____ times (smaller, or larger) when 90 people are infected
2. Calculate rate of spread when entire population is infected
3. Why does this answer make intuitive sense