-aqu 4) (4 pt) Catch-up growth Suppose that initially (at date 0) country A is 3 times richer (in terms of per-capita GDP) than country B, that is 3121(0) yam) a) If country B grows 1% per year faster, on average, than country A, how many years (T) will it take for country B to attain a per-capita income equal to that of country country A? Put differently, nd a date T where 31,, (T) = 959 (T). (Hint: let 9A denote the average growth rate of country A, then 9A + 0.01 would be the average growth rate of country B. Your answer should not depend on what the numerical value of 9A is) =3. b) How much faster (in terms of additional % per year) must country B grow, on average, to catch up with country A in T = 25 years? (Hint: let 9;, denote the average growth rate of country A, and 9A + 6 denote the average growth rate of country B. What is b that makes the catch-up time T = 25?)