It makes sense that the larger the area of a region, the larger  the number of species that inhabit the region. Many ecologists have modeled the species-area relation with a power  function and, in particular, the number of species S of bats  living in caves in central Mexico has been related to the  surface area A of the caves by the equation S = 0.7A^0.3.

(a) The cave called Mission Imposible near Puebla, Mexico, has a surface area of A = 60 m². How many species of bats would you expect to find in that cave?

(b) If you discover that four species of bats live in a cave, estimate the area of the cave.