Simple logging of table access
Assuming that there is an index on the table in question, you could try querying sys.dm_db_index_usage_stats.  It's a view so you will need to specify the database and object_ID of the table you are interested in.  You can query at intervals and store the results to get delta over time.  Look at the MSDN page https://msdn.microsoft.com/en-us/library/ms188755(v=sql.100).aspx for how to interpret the information.