$.$ Write a small C program that copies data from a file A to a file B byte$-$by$-$byte. For different file sizes $1$MB $128$MB $($doubling the file size in each step$),$ record the time your program requires to complete the file copy when using read$()$ and write$()$ system calls. Generate a graph that depicts the program performance. Use the Unix time$(1)$ command.

b$.$ Repeat this experiment, but instead of copying individual bytes, use larger size portions of the file that are copied in each read$()$ and write$()$ system call. For instance, you may choose to copy the file in chunks of $2,4,8,...,1024$ byte units. Use a $128$MB file for each test. Generate a performance graph of transfer size vs execution time and interpret your experimental results.

What do you observe? Why do you think the system shows the observed behavior?