Mathematics
dfbrain
25

In Bear Creek Bay in July, high tide is at 1:00 pm. The water level at high tide is 7 feet at high tide and 1 foot at low tide. Assuming the next high tide is exactly 12 hours later and the height of the water can be modeled by a cosine curve, find an equation for Bear Creek Bay's water level in July as a function of time (t).

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wmcbball31

Ok, let's set up a few variables: W = Water Level (In Feet) t = Time on the clock --------------------------------------------- The model you are looking for is in fact: [latex]W=3\cos { \left( \frac { 1 }{ 3 } t-\frac { \pi }{ 2 } \right) } +4[/latex] You must place the time 1:00pm underneath the angle (3/2)*π radians. Each hour that goes by is equivalent to (1/2)*π radians. ----------------------------------------------- TABLE OF VALUES: When t=0, W=4 [10am] When t=0.5π, W=5.5 [11am] When t=π, W=6.6 [12pm] When t=1.5π, W=7 [1pm] When t=2π, W=6.6 [2pm] When t=2.5π, W=5.5 [3pm] When t=3π, W=4 [4pm] When t=3.5π, W=2.5 [5pm] When t=4π, W=1.4 [6pm] When t=4.5π, W=1 [7pm] When t=5π, W=1.4 [8pm] When t=5.5π, W=2.5 [9pm] When t=6π, W=4 [10pm] When t=6.5π, W=5.5 [11pm] When t=7π, W=6.6 [12pm] When t=7.5π, W=7 [1am] etc... etc... *The information above demonstrates that high tides only shape up every 12 hours.

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