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

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