Please show all steps so i can understand and do myself.

Question 1:

a. Calculate the running time for the following code fragment. Show your work. Algorithm test2 for (i:= 0; i < n; i++) { for (j:=1; j < n; j*=2) { counter := counter +1 } }

b. Indicate whether the first function of each of the following pairs has a smaller, same or larger order of growth (to within a constant multiple) than the second function. Justify your answer 1. n(n2 +1) and 2000 n2 + 34 n 2. ln n and lg n 3. 2 n-1 and 2n 4. 2 n2 and 0.001 n3 2 n