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 !!!