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 = 0, the water level is 19.5 meters (a maximum). At time x = 6.26 hours, the water level is 10.5 meters (a minimum). The period of the function is 12.5 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 water level varies around a midline of (19.5 + 10.5) ÷ 2 = 15 meters, with an amplitude of 4.5 meters. Since it starts at its maximum, model it as y = 15 + 4.5 cos(2πx/12.5). Setting y = 17 gives cos(2πx/12.5) = 2/4.5; the first positive solution is about 2.2 hours. So the correct choice is A, 2.2 hours.
AI-written and checked against the verified answer.