Throughout the day, the depth of water at the end of a dock varies with the tides. the function represents the height, in feet, of the water t hours after midnight. which graph shows the height of the water at the dock at any time after midnight?

You forgot to include the function and the set of graphs from where select the right one.

I did some research and found the function is:

h(t) = 5 cos (0.5t - 2) + 7

The graph for that function is in the figure attached. That is the answer.

To depict the grahp you can use this knowledge:

1) The maximum value of the cosine funcion is 1 and the minimum is - 1

2) Then, the maximum value of h(t) is 5(1) + 7 = 12

And that happens when the argument of the cosine is 0, which means:

0.5t - 2 = 0 => 0.5t = 2 => t = 2 / 0.5 = 4

So the maximum in the graph is the point (4, 12)

3) The minimum value of h(t) is 5(-1) + 12 = - 5 + 12 = 7.

And that happens when 0.5 t - 2 = π => 0.5t = π + 2 = (π + 2) / 0.5 ≈ 10.3

So, the minimum in the graph is the point (10.3, 7)

4) The vertical axis - intercept is when t = 0 => h(0) = 5cos(0 - 2) + 7 ≈ 4.9

With that you can choose the graph from your choices, and the result is the graph attached.

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