It seems about right, below is a graph of the number at sea at any one time. It's not until Aug. 1942 that they first achieve 100 U Boots at sea at the same time.Germany had only.some 57 submarines at the start of the war from what I read, mostly the smaller and more limited Type II coastal U-boats. Had they larger numbers of more capable U-boats early in the war, it might have had an effect on the outcome.
I guess that by 'on patrol' they mean in position and where they are supposed to be. By May 1943, this is 160. The rule of thumb is that you need three times the number for every one that is active. One is 'one patrol', one is either sailing to or returning from position and one is in dock for servicing. There is a list of types including year of production here: List of U-boat types - Wikipedia