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. a) Estimate to the nearest hour the time interval when the boat can be safely secured.
b) Develop a trigonometric function that models the depth of water in meters t hours after midnight.
c) Determine, to the nearest tenth of a meter, the depth of water at noon by applying the function from part b. Noon is 12 hours after midnight.
d) Determine the time to the nearest minute the boat can first be safely secured by using the function from part b.