Problem 4. Asymptotic Bounds Provide tight asymptotic bounds (ie. (-)) on the following. You do not need to explain your bounds. (3 points each) (a) .in/i (b) _i3 (c) l log(n/i) [Hint: Stirling's approximation may be useful (see Wikipedia).] (d) 2 Vn+log n e) The number of bits needed to write 10" in binary. (f) Planet X has a current population 1 billion. Assuming that the population of planet X doubles every year, give an asymptotic bound on the population of planet X in 100 years from now