Question

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?

Answer 1

b

Explanation:

Answer 2

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.