Answer the following questions.

Question 1- Hardware vendor XYZ Corp. claims that their latest computer will run 256 times faster than that of their competitor, Prunes, Inc.

If the Prunes, Inc. computer can execute a program on input of size n in one hour, what size input can XYZ's computer execute in one hour for each algorithm with the following growth rate equations?

n n^2    2^n

Question 2- What sequence of characters would you push onto a stack, so that when you pop the characters off they spell "desserts".

Question 3- Determine ? (Theta) for the given code fragments in the average case. Assume that all variables are of type int.

sum = 0; 

for (i=1; i<=n; i++) 

for (j=1; j<=n; j *= 2) 

sum++;

I am stuck on how to solve these problems correctly. Please give a detailed answer so that I may learn from it. Thank you!