Some of the highest tides in the world occur in the Bay of Fundy on the Atlantic Coast of Canada. At Hopewell Cape the water depth at low tide is about 2.0 m and at high tide it is about 12.0 m. The natural period of oscillation is about 12 hours and on June 30, 2009, high tide occurred at 6:45 am. Find a function involving the cosine function that models the water depth Dstd (in meters) as a function of time t (in hours after midnight) on that day

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mateoe1 mateoe1 · Answer 1 · 2019-09-26T05:07:11+02:00

Answer:

[tex]y = 5cos(\frac{\pi }{12}(t-6.75))+7[/tex]

Step-by-step explanation:

You have been asked to find the values in the function:

[tex]y=Acos(B(t+C))+D[/tex]

First, calculate A, called the amplitude, as half the value from peak to peak (from lowtide to high tide):

[tex]A = (12-2)/2=5[/tex]

Then, calculate the vertical shift D as the average value between the high tide and lowtide:

[tex]D = (12+2)/2=7[/tex]

Then, if P is the natural period of the tide, you can calculate B, or the frequency as:

[tex]B=\frac{\pi }{P}=\frac{\pi }{12}[/tex]

Finally you need to find C or the phase shift thinking that for negative values, the function is shifted (displaced) to the right.

C=-6.75