Tide Modelling

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  • Topic: Mathematics, Inverse function, Leonhard Euler
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Math Honors 2: Portfolio Task 2 (due at 7:30 a.m. May 31 - Block A
OR at 8:30 a.m. June 1 - Blocks C & D)
TIDE MODELLING

Description
The Bay of Fundy in Nova Scotia, Canada is deemed to have the greatest average change in tide height in the world. In the table below data is presented from December 27 2003 using Atlantic Standard Time (AST). The heights were taken at Grindstone Island.

In this task you will develop a model function for the relationship between the time of day and the height of the tide. Consider carefully the expectations of a modeling task as you complete your work by referring to the assessment rubric. Method

1. Using a GDC or graphing software, plot the graph of time against height. Describe the result. 2. Use your knowledge of functions to develop two functions that model the behavior noted in the graph. Describe any variables, parameters, and/or constraints for the model. You should: (a) develop a polynomial function, by solving a system of equations using matrices (b) develop a trigonometric function, by analyzing key characteristics of the graph (c) discuss why exponential and logarithmic functions are inappropriate choices to model the height of the tide 3. Draw a graph of each function on the same set of axes as the graph in Step 1. How well does each function fit the data? 4. Modify each of your functions to create a better fit. Describe the issues you had to consider. 5. Good sailors will launch their boats on an outgoing tide (that is when the tide is going out). Use each of your modified functions to determine the times between which a good sailor would have launched a boat on December 27 2003. 6. Use the regression feature of your GDC or software to develop best-fit polynomial and trigonometric functions for this data. Compare these functions with the ones you developed analytically. 7. The table below lists the tide heights for December 28 2003. Does your...
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