3. An emerging country expects that its GDP will grow exponentially in the next decades by a growth rate of k. In the present year, 2021, its GDP (Y, in billions of $) is equal to A. That is, the GDP of the country follows the following function

1. (12 marks) If the countrys aim is to double its GDP in 15 years, what should be the growth rate, k?
2. (8 marks) Given the growth rate you calculated in part a) and assuming that its GDP in 2031 is expected to be 4 (billion $), what is the value of A?