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 to 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= acos(bt+c)+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.