Explanation Given information: The population density of Philadelphia in 1940 was given by the function 60 e − 0.4 t Graph: D ( t ) be the density of population (in persons per mile) at distance t miles from the city center. Therefore, D ( t ) = 60 e − 0.4 t . Ring includes all persons who live between a and b miles from the city center. Hence, a = 0 and b = 5 Thus, by using the total population in a ring around the city center, ∫ a b 2 π t D ( t ) d t Therefore, the number of people (in thousands) who lived within 5 miles of the city center is ∫ 0 5 2 π t ( 60 e − 0.4 t ) d t . ∫ 0 5 2 π t ( 60 e − 0.4 t ) d t = 120 π ∫ 0 5 t ( e − 0.4 t ) d t By using the integration by parts rule, = 120 π ∫ 0 5 t ( e − 0.4 t ) d t = 120 π [ ( t ) e − 0.4 t − 0.4 | 0 5 − ∫ 0 5 ( 1 ) e − 0.4 t − 0

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Chapter 9.5, Problem 11E

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To graph: The population densities for 1900 and 1940 on a common graph, also find the trend of the graph, where the population density of Philadelphia in 1940 was given by the function 60e−0.4t and find the number of people (in thousands) who lived within 5 miles of the city center.

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Chapter 9.5, Problem 10E

Chapter 9.5, Problem 12E

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To graph: The population densities for 1900 and 1940 on a common graph, also find the trend of the graph, where the population density of Philadelphia in 1940 was given by the function 60 e − 0.4 t and find the number of people (in thousands) who lived within 5 miles of the city center.

Solution Summary: The author graphs the population density of Philadelphia in 1940 and the number of people living within 5 miles of the city center.

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To graph: The population densities for 1900 and 1940 on a common graph, also find the trend of the graph, where the population density of Philadelphia in 1940 was given by the function 60e−0.4t and find the number of people (in thousands) who lived within 5 miles of the city center.

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