The depth of water at the end of a pier varies with the tides

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The depth of water at the end of a pier varies with the tides. The low tides occur on a particular day at 2:00 a.m. and 2:00 p.m. with a depth of 1.1 m. The high tides occur at 8:00 a.m. and 8:00 p.m. with a depth of 5.3 m. A large boat needs at least 3 m of water to be safely secured at the end of the pier.

Develop an exact trigonometric function that models the depth of water in meters t hours after midnight.

 

 Note: An exact function does not use decimal approximations.

 

1)Describe the step-by-step process used to determine the exact function from part B, including a discussion on each of the following:

• amplitude

• period

• horizontal translation

• vertical translation

2)Calculate the time to the nearest minute that the boat can first be safely secured by using the function from part B. Explain step-by-step all mathematical calculations, the use of technology, or both.