shoot......Appalachia starts on the Cumberland Plateau in my opinion and the rise up the western slope is about 30 miles east of Nashville on I-40.
I'd say anywhere east of the Carthage-Gordonsville exit on I-40 is the beginning of Appalachia and run straight across to Wilkes Barre North Carolina ...about a 250 mile wide swath from Northern GA and Alabama across to NW South Carolina up thru KY, NC, VA, WV, PA, Ohio, MD and even parts of NY VT, NH and ME but that's just me.
It's irrelevant whether Nashville is 10, 20, or 40 miles from your geographic definition of Appalachia.
Nashville's a thousand miles from Appalachia socio/economically.