# As global warming progresses, more and more ice will melt and

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```					                                     Go with the Flow

As global warming progresses, more and more ice will melt and ocean levels will rise.
Rising ocean levels can cause some serious problems along coastal areas. These
problems become even more severe when the effect is exacerbated by the effect of the
tides. Given the following scenario for tidal action, see if you can determine a
mathematical model to give us the tide’s height for any particular time.

Tides are caused by the interaction of the moon’s gravity on the earth. The water in the
earth’s oceans is attracted toward the moon and “bulges up”, but as the earth rotates and
the moon revolves about it, the relative position of the moon is constantly changing with
regard to any particular coastal area. This causes the tides to “come in” and “go out” on a
regular basis. For the purpose of this exercise, we will say it takes 12 hours for the tide to
go from low tide to high tide and then back to low tide again.

Let’s suppose there is an area that has a tide which behaves in the following way:
The tide comes in 1/12 of its height during the first hour from low tide
The tide comes in 2/12 of its height during the second hour
The tide comes in 3/12 of its height during the third hour
The tide comes in 3/12 of its height during the fourth hour
The tide comes in 2/12 of its height during the fifth hour
The tide comes in 1/12 of its height during the sixth hour and reaches high tide
Then the process begins for the tide going out in the same proportions:
The tide goes out 1/12 of its height during the first hour from high tide
The tide goes out 2/12 of its height during the second hour
The tide goes out 3/12 of its height during the third hour
The tide goes out 3/12 of its height during the fourth hour
The tide goes out 2/12 of its height during the fifth hour
The tide goes out 1/12 of its height during the sixth hour and reaches low tide

This process has taken 12 hours, and then repeats over and over again.

Analyze this situation as before, using the same questions.

   What words or phrases suggest a particular function family?
   What function family do you think would provide a good model for this situation?
Why do you think so?

Be prepared to share your predictions with the class.

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