Let a function y represent the water level in a harbor measured in meters, and let x represent the number of hours since high tide. At time x is equal to 0 , the water level is 19 point 5 meters (a maximum). At time x is equal to 6 point 2 6 hours, the water level is 10 point 5 meters (a minimum). The period of the function is 12 point 5 hours. After how many hours is the water expected to reach a depth of 17 meters for the first time? Round to the nearest tenth of an hour.
The midline is (19.5 + 10.5) ÷ 2 = 15 meters, and the amplitude is (19.5 − 10.5) ÷ 2 = 4.5 meters. Since the level starts at its maximum, model it with y = 15 + 4.5 cos(2πx ÷ 12.5). Setting y = 17 gives cos(2πx ÷ 12.5) = 2 ÷ 4.5; solving for the first positive time gives about 2.2 hours. So the correct choice is D, 2.2 hours.
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