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# Trig Calculus word problem

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The depth of water at the end of a pier varies with the tides. On a particular day, the low tides occur at 2:00 a.m. and 2:00 p.m. with a depth of 2.1 meters. The high tides occur at 8:00 a.m. and 8:00 p.m. with a depth of 6.3 meters. A large boat needs at least 4 meters of water to be safely secured at the end of the pier.

B. Create an appropriately labeled graph of the depth of water from midnight to midnight.
1. Estimate all time interval(s) when the boat can be safely secured, using the graph.

C. Write a trigonometric function that models the depth of water in meters t hours after midnight.
1. Describe the step-by-step process used to determine the function (i.e., amplitude, period, horizontal translation, and vertical translation).
2. Determine the depth of water at noon by applying the function from part C.
3. Determine the exact time the boat can first be safely secured by using the function from part C, showing all work.