# Hard Disk Space (Linear Function)

• Mar 18th 2010, 07:47 AM
MathBane
Hard Disk Space (Linear Function)
The hard disk drive on a computer holds 600 gigabytes of information. That is 600,000 megabytes. The formatting information, operating system, and applications software take up 4000 megabytes of disk space. The operator wants to store on his computer a collection of digitized pictures, each of which requires 2 megabytes of 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 is linear.

(The change in total storage space used is always the same for a change of 1 in the number of pictures that are stored.)

(b) Find a formula to express the total amount of storage space S used on the disk drive as a linear function of the number of pictures n that are stored on the drive.

S(n) =

(I figured that 2n would be the slope... but the intercept is wrong... I thought it would be 600,000 or 596,000.)
• Mar 18th 2010, 08:18 AM
Hello MathBane
Quote:

Originally Posted by MathBane
The hard disk drive on a computer holds 600 gigabytes of information. That is 600,000 megabytes. The formatting information, operating system, and applications software take up 4000 megabytes of disk space. The operator wants to store on his computer a collection of digitized pictures, each of which requires 2 megabytes of 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 is linear.

(The change in total storage space used is always the same for a change of 1 in the number of pictures that are stored.)

(b) Find a formula to express the total amount of storage space S used on the disk drive as a linear function of the number of pictures n that are stored on the drive.

S(n) =

(I figured that 2n would be the slope... but the intercept is wrong... I thought it would be 600,000 or 596,000.)

The answer to (a) is correct.

For (b), don't be distracted by the 600,000 megabytes. This is simply the maximum value of $S$. The important figure is the 4000 megabytes that is needed, even if no pictures are stored.

In other words, if $n = 0, S = 4000$ (where S is measured in megabytes.). This, then, is the intercept.

You're not quite correct in saying that the slope is $2n$. The slope is $2$. So the formula you want is:
$S = 2n + 4000$