Final answer:
The approximate carrying capacity of the island for the penguin population from 1960 to 1975 is around 120 individuals, based on the stabilization of their numbers after initial exponential growth.
Step-by-step explanation:
If the penguin population fluctuates around the carrying capacity of the island from 1960 to 1975, the approximate carrying capacity can be determined from observations of the population's growth pattern. Initially, the population grew exponentially, indicating few limits to growth. However, as resources began to become limited, the growth rate slowed and the pattern of growth became logistic – a sigmoid curve that levels off at the top. The penguin population then stabilized after reaching a certain number, which suggests this is the carrying capacity. Both statements referring to the population reaching a stable number, one at 116 individuals and the other at 120, indicate the carrying capacity of the environment. Since carrying capacity is related to the maximum sustainable population, we can reasonably conclude that the carrying capacity for penguins on the island was approximately 120 individuals based on these observations.