I would like to use the business name Life 101 The name is taken yet the young gal has a total of 20 posts and the last one dates back to 2011. ...

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Hi Somma

Have you already reaching out to the owner of the Life101 account?

Please let me know by typing a response at the top and clicking on send response

Do you already have an active audience and influence in instagram?

OK. If the owner of the Life101 is not responding to your request to possibly yiled her username and give it to you your last option is to report the account  either an impersonator or trademark issue.  Instagram will verify the account of Life101 and also your account . The reason why I'm asking if you have an active influence  enough bearing for you to request a claim to an inactive account.    

Unfotrtunately Instagram don’t take on personal cases.The last option you have is to report the account owner as an impersonator

If a username you want is being used by an account that seems inactive, you can choose an available version of the username to use on Instagram. You can add periods, numbers, underscores or abbreviations to help you come up with a username that's not already in use.

Even if the account will be deleted by instagram due to inactivity  it will not be recycled. Also, not all activities are showing  in IG. It means that if the post you see in piblic shows  2011 it does not mean that the owner is not active coz she might be likin or commenting to other post or just plainly as n observer.  

Issue identified :  use a taken instagram name

Solution Implemented: provide info on how to report for trademark or impersonation report to request to get the IG name| contact the owner of the acccount| provide some other ways like  can adding periods, numbers, underscores or abbreviations to help come up with a username that's not already in use| accepted answer