Suppose the Population Density of a City Is Approximated by the Model

question 97

Multiple Choice

Suppose the population density of a city is approximated by the model $f ( x , y ) = 6000 e ^ { - 0.01 \left( x ^ { 2 } + y ^ { 2 } \right) } , x ^ { 2 } + y ^ { 2 } \leq 25$ , where $x$ and $y$ are measured in miles. Integrate the density function over the indicated circular region to approximate the population of the city. Round your answer to the nearest integer.

• A) 417,127
• B) 417,029
• C) 833,901
• D) 833,903
• E) 416,951

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Definitions:

Transfer Payments

Payments made by governments to individuals without any goods or services being received in return, such as welfare, social security, and unemployment benefits.

Federal Budget Deficit

The amount by which a government's expenditures exceed its tax revenues over a specific fiscal period, leading to borrowing or debt accumulation.

Economic Growth

Growth in the inflation-corrected value of goods and services that an economy outputs over time.

Social Security

The U.S. social insurance program financed by a federal payroll tax that provides disability, retirement, and death benefits.