Answer Happy

For the following questions, you will need the following formula: let Xo be the initial value, X, be the value after t periods and g be the growth rate by period, then Xt = Xo (1 + g)t. You may also need the log properties: log(a³) = blog(a) and log(ab) = log(a) + log(b). The properties imply: log(X) = log(Xo) + tlog(1+g). a. Suppose the initial real per capita GDP for countries A and B is 7 thousand dollars. If the annual growth rates of countries A and B are respectively 3.5% and 5.5%, what is the the ratio XB/XA after 70 years? Round your answer to the nearest first decimal. Number b. Suppose the annual growth rates of countries A and B are respectively 3.5% and 5.5%. How many years it will take for each country to double their respective real per capita GDP? Round your answer to the nearest first decimal. Country A: Number Country B: Number c. Suppose the initial real per capita GDP of countries A, B and C are respectively 10, 10 and 50 thousand dollars. If their annual growth rates are respectively 3.5%, 5.5% and 1.0%, how many years it will take for countries A and B to converge to country C? Round your answer to the nearest first decimal. Country A: Number Country B: Number