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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