For a database application, assume it takes 10 ms to read a block from disk, 1 ms to search for a record in a block stored in memory, and that there is room in memory for a buffer pool of 5 blocks. Requests come in for records, with the request specifying which block contains the record. If a block is accessed, there is a 10% probability for each of the next ten requests that the request will be to the same block. What will be the expected performance improvement for each of the following modifications to the system?

(a) Get a CPU that is twice as fast.

(b) Get a disk drive that is twice as fast.

(c) Get enough memory to double the buffer pool size.

Write a simulation to analyze this problem.