Suppose, a country X has a GDP level of 4, 50,000 and a growth rate of 10% in 2007 (calculated at the end of the fiscal year 2007). The experts predict that the growth of the economy of Country X will gradually slowdown in the coming years. More precisely, they foresee the following growth rates for the future: 2007 - 2010 = 10% 2010 - 2013 = 9% 2013 - 2016 = 7.5% 2016 - 2019 = 5% 2019 - on = 1% Hint: The list above should be read as saying that, for instance, the growth rate from the end of the fiscal year 2007 until the end of 2010 will be 10 %, then from the end of 2010 until the end of 2013 it will be 9% and so on. a) Assuming that the predictions of the experts listed above are accurate, when in the future will Country X's GDP double compared to the GDP level of 2007? [5 points] b) What would your answer for the question in part (a) be if the growth rate from 2019 and on was in fact -1%? Explain your reasoning carefully. [3 points] c) Consider now the more optimistic scenario in which the economy does not slow down and the current growth rate of 10% remains constant in the coming years. How long will it take for the GDP level to double in this scenario? Express your answer in two forms: [2 points] i) in number of years ii) as a fraction of your answer in part (a)