I am not using Backup Exec, however, if you are only doing full backups, and the database is in Full Recovery, Bullk Logged modes, your transaction log will continue grow. The SQL Server backup only backs up enough of the transaction log to give you a consistant backup when restored. Backup Exec most likely does the same.
To truncate your transaction logs, you either need to run a BACKUP LOG [dbname] WITH TRUNCATE_ONLY prior to your full backup or (and this is the preferred choice I would say), run periodic transaction log backups during the day. The tranascation log backups will truncate your transaction loga and keep them from growing constantly.