1. Suppose we have a B-Tree that holds keys and leaves. There are 300 million data records (N), and they are stored in the leaves (lowest level) of the B-Tree. Each leaf contains 100 data records. The leaves are stored only at the bottom level of the tree (below the keys), and each key at the bottom level of keys points to one leaf. The B-Tree has 4 levels of keys counting the root level which has m keys. Except for the bottom level, each key has m child keys. The bottom level keys have leaves (one leaf per key).
   1. Sketch a simple tree like the one on the next page (this is not the same tree you have to do, its just a similar example)
   2. How many leaves are required to hold all the data records?
   3. How many keys are required at the lowest key level of the B-Tree?
   4. What is the branching factor (M) of the B-Tree. Show your work.