I am so glad you asked, jimonroe.
The Google Sync will automatically back up all of the apps that you have installed on your device.
All you need to do is remember the GMAIL email address & password that was used when you set up your phone.
From a computer, Go to play.google.com
Select My Android Apps
Sign in using Google Gmail sign in
Upper left you will see My Android Apps
This will show all apps that have ever been installed with that information.
In addition, from the device you can still go to
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