Concepts: Transformations of functions and findingintercepts.

HMS Nautical Inc.

2200 Seaview Blvd.

North Shore, Hi 09231

Math Class

DeVry University

122^nd and Pecos

Westminster, CO 80241

Dear Students:

I have recently been employed by HMS Nautical Inc to work ontheir submarine program. I have only some basic data to work withand no idea how to use it to get the information I need.

Here is what I know. First, I know that our Subs have a maximumrunning depth of 500 feet below sea level. I also know that a subfunctioning at acceptable levels should be able to reach maximumdepth in 10 minutes. Finally I know that I need to multiply thedecent by a factor of 5 to achieve an accurate model. I also have achart that lists times and depths for the sub.

Time (minutes)	1	5	9	10	11	15
Depth in Meters	-95	-375	-495	-500	-495	-375

Finally, I know that the sub follows a quadratic model when itdescends and then ascends.

I have been told that you will be able to take this data andmake sense of it. I would like a model for the path of thesubmarine as it descends to its running depth and then returns tothe surface. I want to be able to use this model to predict wherethe sub will be at any time during its decent/ascent cycle. I wouldalso like to know after how many minutes I should expect the sub tobreech the surface of the water again.

Please explain clearly how you came up with the model sothat I can repeat the process for new additions to our fleet ofsubmarines. I appreciate any help you can give me in this matter. Iwould like your response returned to me either as a business letteror a narrated PowerPoint presentation.

Sincerely,

Nemo Hook