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 Mision Imposible near Puebla, Mexico, has a surface area of $ A = 60 m^2 $ . 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.