At the beginning of 2003, Mr. Pu, the president of country Ru, set an ambitious goal: Ru's real GDP must be doubled in 10 years, by 2013. In 2003, Ru's real GDP was equal to 20.

1. At what rate (let's call it the "target" rate) did the economy of Ru have to grow in order to achieve Mr. Pu's goal? How long would it take for the economy of Ru to double if it grew at 5% per year? Hint: use the rule of 70.

2. The economy of Ru was off to a good start and was growing at the target rate for 5 years, from 2003 until 2008, when the world economic crisis arrived. As a result of the crisis, in 2008 and 2009 real GDP was growing at just 1% per year. Furthermore, following the two crisis years, the economy could only sustain the annual growth rate of 2%. Write down the formula to calculate the level of Ru's real GDP in 2013.Hint: use the constant growth rule repeatedly. In case you are curious, if you evaluate that formula, the answer will be roughly 30.

3. On a ratio scale of your choice, sketch two trajectories: the hypothetical evolution of Ru's real GDP according to the target rate and its actual evolution from 2003 until 2013.

Another ambitious goal set by Mr. Pu at the beginning of 2003 was to increase the living standards of Ru's people. Specifically, the goal was to catch up with country Po in terms of the level of real GDP per capita by 2017. In 2003, the population of Ru was 10. The real GDP per capita in Po was equal to 3 (measured in units comparable to Ru's GDP figure from part 1).

4. If Po's real GDP grew at 6% per year and its population grew at 1% per year, what would be its (approximate) level of real GDP per capita in 2017?

5. If Ru wants to catch up with Po in 2017, what would its annual growth rate of real GDP per capita have to be? You do not have to calculate the exact value, just provide the formula that allows you to do it.