or the following questions, you will need the following formula: let Xo be the initial value, X, be the value after t periods and g the growth rate by period, then X₁ = Xo(1+g)¹. ou may also need the log properties: log(a) = blog(a) and log(ab) = log(a) +log(b). The properties imply: log(X₂) = log(X₁) + tlog(1+g). a. Suppose the initial real per capita GDP for countries A and B is 14 thousand dollars. If the annual growth rates of countries A and B are respectively 2.8% and 4.8 %, what is the the ratio X/X₁ after 51 years? Round your answer to the nearest first decimal. Number b. Suppose the annual growth rates of countries A and B are respectively 2.8% and 4.8%. 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 2.8%, 4.8% 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

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