Step 1: Identify Cave 15 and its patronage.
Cave 15 at Ellora is known as the Dashavatara (Ten Avatars of Vishnu) cave. Its construction is attributed to the Rashtrakuta dynasty, specifically during the reign of Dantidurga.
Step 2: Determine the historical period of the patrons.
The Rashtrakuta dynasty ruled over large parts of the Indian subcontinent between the 8th and 10th centuries C.E. The reign of Dantidurga, who commissioned the transformation of this cave from a Buddhist vihara to a Hindu temple, was in the mid-8th century (circa 735-756 C.E.). Therefore, the carvings belong to the 8th century C.E.