Please explain step by step

(a) (b) What is the amortized analysis and when can it be used? Assume that the initial size of a vector is 1 and you want to insert 32 items in the vector. no enough memory then a resize function is called and it doubles the amount of the memory assigned to the vector. If there is (c) How many times should the resize function be called to place all the items into the vector and keep extra space for a few more elements? d) How many additional copy operations are performed to place all the items in the vector? (e) What is the amortized (average cost) of one insert (push_back) operation? Provide answers to all the questions above when the input size of the vector is n