Tide Modelling

1587 Words Apr 16th, 2012 7 Pages
IB Mathematics Standard Level Portfolio Assignment Task I
Tide Modeling
Kelvin Kwok

In this modeling assignment, I will develop a model function for the relationship between time of day and the height of the tide. I will first show the data in a table form copied from the assignment sheet. Then I will use the data to construct a scatter graph of time against height, then I will develop a function that models the behavior noted in the graph analytically, and describe any variables, parameters or constraints for the model. In the end I will modify the same model using the regression feature of graphing software to develop a best-fit function for the data. This modeling task will allow me to find out what is the best time that a good
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And for the value of C which is the horizontal translation, by trial and error method, I have found that by + π12 to the function which translate the function to the left along the x-axis.

And D is the principal axis, as the min. value and max. value has already changed, so the new value for D would be 12.15+0.82=6.475

Hence we will get a modified function y=5.675sinx2+π12+6.475

Diagram3 Graph of the modified function y=5.675sinx2+π12+6.475 in method4

From diagram 3, we can see that the modified function has passed through 11 data points in total, which is 3 times more than the old function. So it is obvious a better fit to the data points.

Method 5: Decide what time a good sailor should launch their boat based on the model in method 4

An outgoing tide is a receding tide , i.e. a tide that decreases from it’s max height(crest) to its min. height(trough), from our observations on the graph in method 4 , the max. height of the tide occurs at 2.6 hours after midnight and 15.2 hours after midnight which is 2:36am and 3:12pm respectively. However, it’s more sensible to launch a boat in day light rather than in the dark, therefore the best for a good sailor to launch a boat would be 3:12pm. But since the function modeled in part 4 is not a perfit fit, therefore the perdiction of the best time to launch a boat is a theoretical guess.
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