Chapter 3.2, Problem 11E

Reminder Round all answer to two decimal places unless otherwise indicated.

Digitized Pictures on a Disk Drive The hard disk drive on a computer holds $800$ gigabytes of information. That is $800,000$ megabytes. The formatting information, operating system, and applications software take up $6000$ megabytes of disk space. The operator wants to store on his computer a collection of digitized pictures, each of which requires $2$ megabytes of storage space.

a. We think of the total amount of storage space used on the disk drive as a function of the number of pictures that are stored on the drive. Explain why this function in linear.

b. Find a formula to express the total amount of storage space used on the disk drive as a linear function of the number of pictures that are stored on the drive. (Be sure to identify what the letters you use mean.) Explain in practical terms what the slope of this function is.

c. Express using functional notation the total amount storage space used on the disk drive if there are $350$ pictures stored on the drive, and then calculate that value.

d. After putting a number of pictures on the disk drive, the operator executes a directory command, and at the end of the list, the computer displays the message 769, 000, 000, 000 bytes free. This message means that there are $769,000$ megabytes of storage space left on the computer. How many pictures are stored on the disk drive? How many additional pictures can be added before the disk drive is filled?