A park ranger is searching for bears in a region of the park where on average there are 12 bears per square mile.  The bears are solitary independent creatures, so it is reasonable to assume that the numbers of bears in disjoint regions are independent unknowns and that the number expected in any region is proportional to the area of the region.  The ranger can also assume that in a very tiny region, say a square inch, it is impossible to find more than one bear.  How much area (in square miles) does he expect to have to search in order to find 15 bears?

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Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
Problem 7ECP: The kinetic energy E of an object varies jointly with the object’s mass m and the square of the...
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A park ranger is searching for bears in a region of the park where on average there are 12 bears per square mile.  The bears are solitary independent creatures, so it is reasonable to assume that the numbers of bears in disjoint regions are independent unknowns and that the number expected in any region is proportional to the area of the region.  The ranger can also assume that in a very tiny region, say a square inch, it is impossible to find more than one bear.  How much area (in square miles) does he expect to have to search in order to find 15 bears?

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