First, since you're only getting one element from stat, you might as well stick it in a scalar instead of an array. To see if a file was modified more than seven days ago, just get the current time and compare.
my $mtime = (stat $tapes)[9];
my $now = time;
if( $mtime < ( $now - 604800) ) {
print "$tapes is more than seven days old.\n";
}