On February 10, 1990, high tide in Boston was at midnight. The water level at high tide was 9.9 feet; later, at low tide, it was 0.1 feet. Assuming the next high tide is exactly 12 hours later and that the height of the water is given by a sine or cosine curve, find a formula for water level in Boston as a function of time. On Feb 10, when is the water level 6.5 feet high? On Feb 10, what is the water level at 10 am? 4pm?

a) Model

b) The tide will be at 6.5 ft high at 2:24 am (going down).

As the tide will rise again, the tide will be again at 6.5 ft high at 9:36 am (going up).

c) H(10 am) = 7.45

H(4 pm) = 2.55

Step-by-step explanation:

We can model this as a sine or cosine wave, for which we will calculate its parameters by the data given.

The model we will use is:

t will be in hours, starting from midnight (t=0)

1) We know that at midnight happens the high tide. That means that

2) Six hours later (t=6) happens the low tide (0.1 ft)

Now that we have calculated all the parameters, the model for the height of the tide is:

On Feb 10, when is the water level 6.5 feet high?

The tide will be at 6.5 ft high at 2:24 am (going down).

As the tide will rise again, the tide will be again at 6.5 ft high at 9:36 am (going up).

On Feb 10, what is the water level at 10 am? 4pm?

At 10 am is t=10:

At 4 pm, is t=12+4=16

step-by-step explanation: