The Department of Forestry is studying the bark beetle infestation in the Helena

Question

The Department of Forestry is studying the bark beetle infestation in the Helena National Forest, so they decide to put out traps in different locations to measure the number of beetles. The traps emit an odor that attracts the beetles and then captures them. The Department estimates that in 24 hours each trap captures 50% of all the beetles within a 25 meter radius. They lay out the traps in a grid with the number of beetles recorded in each trap after 24 hours given in the table below, where x and y are coordinates in the forest (given in meters).

What is the approximate number of beetles per square meter at coordinates (3000, 500)? ________

What is the best possible estimate of the number of beetles in the rectangle with corners at (1000,500), (1000,1000), (3000,500), and (3000, 1000)? ________

Explanation / Answer

1.number of beetles oer square at coordinates(3000,500)= 112*2(as each trap captures 50%of beetles, so double the value given that is the excat number of beetles present.)

=224 in 25sq metre radius.we need per squre.so divide it by approximatly by 25 we get

224/25=8.96 =9(round off)/per square metre

2.total number of beetles at the corner (we take only one fourth of the 25mt sq circle.so

adding all corner values and divideing by 4 we get=52+50 +112+110=324/4=81

81 is the number of beetles in the rectangle . but its only 50%.so to make it 100% multiply by 2 we get=81*2=162.

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