probably you'd notice when it was busy. Why would you let your log grow so large? Eventually you will run out of space and you have no option than to backup your log and truncate it but why wait until that time.
MWilkes, you are correct. The growing of the file goes a little like this:
step one: Realize you are out of space
step two: Grow the file to the size specified (10% of 14 GB is a pile of disk, too)
step three: Wait until the entire addition to the file has been prepared for use by SQL Server.
Since this is the log portion that is growing, all transactions waiting to write to the transaction log are queued up waiting for new space in the transaction log.
To get a sense of how long this takes, create a database 1.4 GB in size. You will probably see an eerie correlation in times.
As a side note, I usually keep all of my file growths down to 5-50 MB depending on the system and how quickly it grows (but that is just a personal preference).