ark in ▁Pro ctor , ▁Long ▁C ave , ▁commercial ized ▁as ▁Grand ▁Avenue ▁Ca ver ns , ▁and ▁Pro ctor ▁C ave . ▁The ▁city ▁was ▁pl atted ▁and ▁formally ▁incorpor ated ▁under ▁that ▁name ▁in ▁ 1 8 7 1 . ▁ ▁In ▁ 1 9 3 8 , ▁the ▁name ▁was ▁changed ▁to ▁Park ▁City ▁to ▁avoid ▁confusion ▁with ▁Glasgow . ▁ ▁Geography ▁Park ▁City ▁is ▁located ▁in ▁western ▁Bar ren ▁County ▁at ▁ ▁( 3 7 . 0 9 4 1 8 1 , ▁- 8 6 . 0 4 8 3 0 9 ). ▁U . S . ▁Route ▁ 3 1 W ▁passes ▁through ▁the ▁center ▁of ▁the ▁city , ▁and ▁Inter state ▁ 6 5 ▁cut s ▁through ▁the ▁north west ▁corner , ▁with ▁access ▁via ▁Exit ▁ 4 8 ▁( K ent ucky ▁Route ▁ 2 5 5 / M amm oth ▁C ave ▁Park way ). ▁The ▁CS X ▁Transport ation ▁rail ▁line ▁( former ▁L & N ) ▁also ▁passes ▁through ▁the ▁center ▁of ▁the ▁city . ▁ ▁According ▁to ▁the ▁United ▁States ▁Census ▁Bureau , ▁the ▁city ▁has ▁a ▁total ▁area ▁of ▁, ▁of ▁which ▁, ▁or ▁ 0 . 2 5 %, ▁is ▁water . ▁ ▁Dem ograph ics ▁ ▁As ▁of ▁the ▁census ▁of ▁ 2 0 0 0 , ▁there ▁were ▁ 5 1 7 ▁people , ▁ 2 3 7 ▁households , ▁and ▁ 1 4 2 ▁families ▁res iding ▁in ▁the ▁city . ▁The ▁population ▁density ▁was