Question: Refer to a colony of bats which flies out of a cave each night to eat insects. To estimate the colony's size, a naturalist counts samples of bats at different distances from the cave. Table 8.3 gives n, her count per hectare, at a distance r km from the cave. For instance, she counts 300 bats in one hectare at the cave's mouth, and 219 bats in one hectare one kilometer from the cave. The bat count r km from the cave is the same in all directions. [Note that 1 km2 = 100 hectares, written 100 ha.]
Letting n = f(r), write an integral in terms of f representing the number of bats in the cave. Assume that bats fly no farther away than 5 km from the cave. Do not evaluate the integral.