Researchers found a close correlation between an index of universal health care (UHC) and per capita Gross Domestic Product (GDP) given by the equation U = 8.9603 ln x - 13.911, where U is the index of UHC on a scale from 0 to 100 (with scores 80 or above listed as “ ≥ 80”) and x is per capita GDP (in 2016 U.S. dollars).

(a) The U.S. per capita GDP in 2017 was $59,531.66. Find the predicted UHC index.
(b) Repeat part (a) for Pakistan, with a per capita GDP of $1547.85.
(c) Repeat part (a) for Vietnam, with a per capita GDP of $2342.24.
(d) The U.S. UHC index is given as  “ ≥ 80”. Find the predicted per capita GDP for a country with a UHC index of 80.
(e) Repeat part (d) for Pakistan, with a UHC index of 40.
(f) Repeat part (d) for Vietnam, with a UHC index of 73.