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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Population Density The population density (in people per square mile) for a coastal town on an island can be modeled by

f ( x , y ) = 5000 x e y 1 + 2 x 2 where x and y are measured in miles. What is the population inside the rectangular area defined by the vertices (0, 0), (4, 0), (0, −2), and (4, −2)? Is the average population density of the town more than 500 people?

To determine

To calculate: The pollution inside the rectangular area defined by the vertices (0,0),(4,0),(0,2),(4,2) for given the population density (in people per square mile) for a coastal town can be modeled by f(x,y)=5000xey1+2x2.

Explanation

Given information:

The population density (in people per square mile) for a coastal town can be modeled by

f(x,y)=5000xey1+2x2.

Where x and y are measure in miles.

Formula used:

The average value of integral function z=f(x,y) over the region R with area A is

Average value=1ARf(x,y)dxdy

Calculation:

The population density function;

f(x,y)=5000xey1+2x2

Now the integrate the population for limits 0x4 and 2y0,

Pollution=20045000xey1+2x2dxdy=20[5000ey(4x)1+2x2]04dy=125020ey[ln|1+2<

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