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Periodic Functions & Applications – “Tide’s out!”

Bevan Dias Mr. O’Keefe 12A

Year 12 Mathematics B

Year 12 Mathematics B, Periodic Functions & Applications

“Tide’s out!”

Table of Contents 1.0 Water-­‐depth data ..................................................................................................... 3 2.0 Graph of water depth against time .................................................................... 3 Water Depth vs. Time ............................................................................................................................. 3

3.0 Developing a function ............................................................................................ 4 3.1 3.2 3.3 3.4 3.5

Linear Function ................................................................................................................ 4 Quadratic function .......................................................................................................... 5 Cubic function ................................................................................................................... 6 Sinusoidal function ......................................................................................................... 7 Comparison ........................................................................................................................ 8

4.0 Using the function .................................................................................................... 9 4.1 Test 1 .................................................................................................................................... 9 4.2 Test 2 .................................................................................................................................... 9 4.3 Test 3 ................................................................................................................................. 10

5.0 Assumptions and Validity .................................................................................. 11 5.1 Assumptions vs. Effects .................................................................................................. 11 5.2 Validity ................................................................................................................................. 11

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Year 12 Mathematics B, Periodic Functions & Applications

“Tide’s out!”

1.0 Water-­‐depth data

The table below contains tide data from Portland (Victoria) on the 1st of January 2014.

Table 1: Data of tidal movement from 12am -­‐ 7am.

Hours after midnight 0 1 2 3 4 5 6 7

Depth (m) 6.783 6.046 4.593 3.107 1.911 1.007 0.489 0.687

2.0 Graph of water depth against time Water Depth vs. Time

Figure 1: Graph of water depth against time.

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Year 12 Mathematics B, Periodic Functions & Applications

“Tide’s out!”

3.0 Developing a function

This section of the report will deal with developing a function that best models the movement of the tides in Portland, Victoria. Four types