6 ) if a country has GDP equal to A it will have its GDP equal to Aert after I years if it grows at a rate of 10or %. Suppose two countries, Pand Q, have initially their GDPs as follows: Yp = $ 1. 4 trillion YQ = $ 12.0 trillion The growth rates are (p = 0.D] and C= 0.02 per year. After how many years will the two countries have the same GDP ? 7) A firm produces Q units of a product and sells them for a price given by P=1000 - -Q. The cost of production is C = 800 + 3 Q. Ta) Calculate the profit-maximizing quantity that the firm should produce .76) Suppose the government imposes a tax on the firm's product of $10 per ton. Calculate the new profit- maximizing quantity. 8 ) Prove the following equalities: 8a) En x - 3 = In (x/23) 8b ) Z lx - 3, but - In ( x+ 1 ) = en x X+ 1 8 ) 2 lux + 3 - In(ex ) = 0 9 ) if GDP doubles in 15 years , what must be the average annual rate of growth ? ( Use the precise method . ) 10 ) Solve the following equations for x : 10) p= pax- 6 lob) e-a = 10 loc ) =