What is the purpose of the paean?
to honor the gods
to entertain the audience
to create conflict
to provide exposition

The purpose of the paean is to honor the gods. (First option).

According to Greek mythology, they honored and respect God so much. Greeks have a strongly believed in god or goddesses, they used stories about it to tell and explain the unknown things that happened around them such as the moon, the sun, and stars.

That being said, the Paean is a song or a hymn used to be thankful about anything, it is used to show appreciation/ adulation. The song was sung by the Greek population to any Grek god or goddesses.

The answer is to honor the gods.  The paean was a song of thanks giving usually sung by a chorus.  It was sung to any Greek God.  Apart from honoring the gods, it also was sung to avert misfortune and protection from disease.  

c. wright mills's sociological imagination suggest investigating to explain this increase?