What is the ethnographic technique that might be used if the anthropologist were interested in studying a culture over a long period of time-perhaps to better understand issues of social change and cultural adaptation?

Longitudinal research

Explanation:

Longitudinal research: In psychological research, the term longitudinal research is defined as one of the types of observational research methods whereby a researcher gathers a particular data related to the same participants of subjects who have been involved in the study repeatedly over a specific period.

Longitudinal research design can be extended from weeks, months and even to years and it entirely depends on the researcher's interest or the study demand.

In the question above, the given statement represents longitudinal research.