A message in a bottle is floating on top of the ocean in a periodic manner. The time between periods of maximum heights is 20 seconds, and the average height of the bottle is 21 feet. The bottle moves in a manner such that the distance from the highest and lowest point is 8 feet. A Cos function models the movement of the bottle's height in relation to time. Part A: (2 points) Identify the amplitude (in feet) and period of the function (in seconds) that could model the height of the bottle as a function of time, t. State, in complete sentences, how you know. Part B: (4 points) Assuming that at t = 0 the message in a bottle is at its average height and moves up after, identify the values of a, b, c, and d for the function y=a cos(btc) +d that is described by the scenario. Show all work. Part C: (2 points) Write the complete equation of the function. Part D: (2 points) Without looking at the graph of the function, calculate how many seconds it takes to reach its lowest height? Show all work.