Question

The depths of water, at the edge of a pier, at different times of day, are represented by the table below. Which of the following functions best models the depths of the water?

Answer 1

The best answer is C) y=4.75 * cos(0.52x - 2.08) + 7.65

Unfortunately, the two only ways to solve this problem are to either graph all the options or plug in time values for x and see which agrees the most with the tide chart. Both are time-consuming, but I chose to graph each one with a graphing application.
Plugging in a few values for x confirms that C is the best function.
12pm (x=0)
y = 4.75 * cos(0 - 2.08) + 7.65
y = 5.334
2pm (x=2)
y= 6.5
4pm (x=4)
y=12.4
It is not a perfect representation, but the shape of the graph and closeness to the points given is the best of the four options provided.