Explanation It is given that the population of community is 100,000. The variable y denotes the number of people affected by the infectious disease. The number of people who have the infectious disease will be increased as time goes. Thus it is denoted by d y d t . The variable y growing at a rate proportional to the product number of people who all have the disease and the number of people who do not have the disease. Here, y takes the number of people affected by the disease, thus the people not affected by the disease will be taken as 100 , 000 − y . The rate is proportional to product of y and 100 , 000 − y

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Differential Equations

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Chapter 9.2, Problem 12E

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To write: The differential equation that describes statement “ In a community of 100,000, the number of people y who have contracted an infectious disease is growing at a rate proportional to the product of the number of people who have contracted the disease and the number who have not ”.

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Chapter 9.2, Problem 11E

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The differential equation that describes statement “ In a community of 100,000, the number of people y who have contracted an infectious disease is growing at a rate proportional to the product of the number of people who have contracted the disease and the number who have not ”.

Solution Summary: The author explains the differential equation that describes the given statement. The variable y denotes the number of people affected by the infectious disease.

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To write: The differential equation that describes statement “ In a community of 100,000, the number of people y who have contracted an infectious disease is growing at a rate proportional to the product of the number of people who have contracted the disease and the number who have not ”.

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