1. Assume that a program runs in f(n) microseconds, where f(n) is the function given on the left. Fill in how large an input n can be calculated, given each of the runtimes given along the top. I have filled in two values for you. You do not need to fill in every box, but should have at least of every row filled in, and at least half of the rows complete 1 second 1 minute 1 hour 1 day 1 month 1 year lgn 12 10 nlgn 1000 2n Show some calculations, or some of your code if you use code. Which row is the most difficult to compute, and why? Do you have any non-integer answers? 2. Find a simple formula for (2k-1). Prove your answer. 3 Find a formula for the product T14*/2. Prove your answer. 4. Give an asymptotically tight bound forkwhere r 0 is constant