4 2 . ▁In ▁the ▁ 1 9 3 0 s , ▁de pressed ▁conditions ▁in ▁the ▁coal ▁fields ▁resulted ▁in ▁a ▁loss ▁of ▁population ▁that ▁continued ▁through ▁the ▁ 1 9 6 0 s . ▁Prov idence ' ▁economy ▁remains ▁tied ▁to ▁coal ▁and ▁agricult ure . ▁ ▁Geography ▁Prov idence ▁is ▁located ▁at ▁ ▁( 3 7 . 3 9 8 3 8 9 , ▁- 8 7 . 7 5 7 0 7 7 ) ▁The ▁city ▁is ▁concentr ated ▁around ▁the ▁intersection ▁of ▁Kentucky ▁Route ▁ 1 0 9 ▁and ▁Kentucky ▁Route ▁ 1 2 0 , ▁approximately ▁ ▁north west ▁of ▁Mad ison ville . ▁ ▁The ▁Trade water ▁River ▁flows ▁just ▁west ▁of ▁the ▁city , ▁and ▁the ▁Web ster - H op kins ▁county ▁line ▁lies ▁just ▁to ▁the ▁sout heast . ▁ ▁U . S . ▁Route ▁ 4 1 A ▁passes ▁through ▁the ▁eastern ▁part ▁of ▁Prov idence . ▁ ▁Dem ograph ics ▁ ▁As ▁of ▁the ▁ 2 0 0 0 ▁census , ▁there ▁were ▁ 3 , 6 1 1 ▁people , ▁ 1 , 4 8 7 ▁households , ▁and ▁ 1 , 0 2 9 ▁families ▁res iding ▁in ▁the ▁city . ▁The ▁population ▁density ▁was ▁ 5 8 7 . 2 ▁people ▁per ▁square ▁mile ▁( 2 2 6 . 7 / km ²). ▁There ▁were ▁ 1 , 7 5 4 ▁housing ▁units ▁at ▁an ▁average ▁density ▁of ▁ 2 8 5 . 2 ▁per ▁square ▁mile ▁(