Final answer:
Without the specific graph in the context, it is not possible to infer the relationship between population size and the empire's physical size in ancient Mesopotamia; hence, the graph does not provide enough information.
Step-by-step explanation:
The population trends and the size of an empire in ancient Mesopotamia can be better understood when considering various socio-economic factors. The historical texts indicate that urban populations in ancient cities like Sumer and Uruk ranged between 10,000 and 50,000 inhabitants, with larger cities like Rome reaching 650,000. Growth constraints such as adequate sewage control, food supply, and transportation limited urban expansion. Also, evidence suggests that while Mesopotamian empires were engaged in warfare and territorial defense, their ability to manage large populations and territories was hampered by frequent rebellions and external threats from nomadic groups. Agricultural productivity through irrigation facilitated urban development, with most people engaged in agriculture and animal husbandry, even though a majority lived in urban areas.
In the context of the information presented, without a specific graph to examine, it is not possible to accurately determine the relationship between population size and the empire's physical size. Therefore, the correct answer to the student's question would be 'd) The graph does not provide enough information to make an inference.'