Concept explainers
Spread of disease. An infectious cold virus spreads in a community at a rate R (per day) that is jointly proportional to the number of people who are infected with the virus and the number of people in the community who are not infected yet. After the tenth day of the start of a certain infection, 15% of the total population of 20,000 people of Pollutville had been infected and the virus was spreading at the rate of 255 people per day.
a. Find the constant of proportionality, k.
b. At what rate is the disease spreading when one-half the population is infected?
c. Find the number of people infected when the rate of infection reached 95 people per day.
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