Studies indicate that t years from now the population of a c

Studies indicate that t years from now, the population of a certain country will be p = 0.2t + 1, 500 thousand people, and that the gross earnings of the country will be E million dollars, where E(t) = Squareroot 9t^2 + 0.5t + 179 Express the per capita earnings of the country P = E/p as a function of time t. (Take care with P the units.) What happens to the per capita earnings in the long run (as t rightarrow infinity)?

Solution

a) p = 0.2t + 1500

E(t) = sqrt( 9t^2 + 0.5t + 179)

Per capita earnings: P = E/p = sqrt(9t^2 +0.5t +179)/(0.2t +1500)

b) Per capita earnings: P = E/p = sqrt(9t^2 +0.5t +179)/(0.2t +1500)

t ---> inifinty

Divide numerator and denominator by t

E/p =[ sqrt(9 +0.5/t +179/t^2)]/( 0.2+1500/t) as t ---> infinity

E/p = sqrt(9)/0.2 = 3/0.2 = 15 thousand = 15000