Given: y = A cos(Bx − C) + D. The depth of water at the end of a pier varies with the tides. High tide = 4 a.m. w/ a depth of 6 meters. Low tide = 10 a.m. w/ a depth of 2 meters.
A. Model the problem by using the given trigonometric equation to show the depth of the water t hours after midnight, showing all your work.
B. Solve the problem by finding the depth of the water at noon, explaining your reasoning.
C. A large boat needs at least 4 meters of water to secure it at the end of the pier. Determine what span of time after noon, including both a starting and ending time, the boat can first safely be secured, justifying your answer.