After looking at other questions and my textbook, I seem to get some confusion. I do get that when there is a polynomial algorithm of NPC, there is a polynomial algorithm for a NP problem. But the statement describing reduction seems obscure to me at least in the beginning of my studies in computational complexity. So, can we transform an exponential algorithm for NPC (which we have) into an exponential algorithm for another non-NPC NP problem in polynomial time? 
Can an exponential algorithm for an NPC problem be transformed into an algorithm for other NP problems in polynomial time?
complexity theory;terminology;np complete;reductions