In: Math
Dear Students:
I have recently been employed by HMS Nautical Inc to work on their submarine program. I have only some basic data to work with and 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 maximum running depth of 500 feet below sea level. I also know that a sub functioning at acceptable levels should be able to reach maximum depth in 10 minutes. Finally I know that I need to multiply the decent by a factor of 5 to achieve an accurate model. I also have a chart 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 it descends and then ascends.
I have been told that you will be able to take this data and make sense of it. I would like a model for the path of the submarine as it descends to its running depth and then returns to the surface. I want to be able to use this model to predict where the sub will be at any time during its decent/ascent cycle. I would also like to know after how many minutes I should expect the sub to breech the surface of the water again.
Please explain clearly how you came up with the model so that I can repeat the process for new additions to our fleet of submarines. I appreciate any help you can give me in this matter. I would like your response returned to me either as a business letter or a narrated PowerPoint presentation.
Sincerely,
Nemo Hook
HMS Nautical Inc.