SOLUTION: The tide, or depth of the ocean near the shore, changes throughout the day. The depth of the Bay of Fundy can be modeled by d=35-28cos(pi/6.2)t, where d is the depth in feet and t
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Question 457399: The tide, or depth of the ocean near the shore, changes throughout the day. The depth of the Bay of Fundy can be modeled by d=35-28cos(pi/6.2)t, where d is the depth in feet and t is the time in hours.
a. consider a day in which t=0 represents 12:00 am. For that day, when do the high and low tides occur?
b. At what time(s) is the water 3.5 feet?
We find the period of that function as that is the number of
hours from the time the ocean is a certain number of feet
deep until it is that same number of feet deep again.
The period of that function is or
= 12.4 hours.
Low tide is when t=0 or midnight or 12:00AM. So there will
be another low tide again at 12.4 hours later or t=12.4 at
12:24PM. Half-way between those two low tides there will be a
high tide and that will be at t=6.2 hours after midninght, at
6:12AM. 12.4 hours later there will be another high tide at
t=18.6 hours after midnight and that will be at 6:36PM.
The low tide is when t=0, substituting t=0 in the equation
d = 35 - 28cos(pi/6.2)t
d = 35-28cos(pi/6.2)0
d = 35-28cos(0)
d = 35-28(1)
d - 35-28
d = 7
So the lowest possible depth is 7 feet, so it will never be
3.5 feet there. The green line on the graph is at 3.5 feet
and we see that the ocean there never gets that shallow.
So there is no solution to the b part.
Edwin
