In the spirit of TMTOWTDI ... and in the spirit of "How do I do X with Y", I present: "How do I do X ... with X?":
my @info = stat $tapes;
print 'this file hasn't been modified in a while' if -M _ > 7;
The -M function was written specifically for this - as long as you have a short-running script. That's becasue -M compares the modification time to the time that your script started. If you have something running in a persistant environment (e.g., mod_perl), this is probably not what you want. Cron jobs, however, would be somewhere that this just makes things easier.