a message in a bottle is floating on top of the ocean in a periodic manner. the time between periods of maximum heights is 24 seconds, and the average height of the bottle is 8 feet. the bottle moves in a manner such that the distance from the highest and lowest point is 4 feet. a cosine function can model the movement of the message in a bottle in relation to the height. part a: determine the amplitude and period of the function that could model the height of the message in a bottle as a function of time, t. (5 points) part b: assuming that at t