Some of the highest tides in the world occur in the Bay of Fundy on the Atlantic Coast of Canada. At Hopewell Cape the water depth at low tide is about $2.0 \mathrm{~m}$ and at high tide it is about $12.0 \mathrm{~m}$. The natural period of oscillation is about 12 hours and on a particular day, high tide occurred at $6: 45$ AM. Find a function involving the cosine function that models the water depth $D(t)$ (in meters) as a function of time $t$ (in hours after midnight) on that day.
Added by Fred G.
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The natural period of oscillation for the Bay of Fundy is about 12 hours. Therefore, the function we are looking for will have a period of 12 hours. Show more…
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Some of the highest tides in the world occur in the Bay of Fundy on the Atlantic Coast of Canada. At Hopewell Cape the water depth at low tide is about 2.0 $\mathrm{m}$ and at high tide it is about 12.0 $\mathrm{m} .$ The natural period of oscillation is about 12 hours and on June $30,2009,$ high tide occurred at $6 : 45$ AM. Find a function involving the cosine function that models the water depth $D(t)$ (in meters) as a function of time $t$ (in hours after midnight) on that day
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Some of the highest tides in the world occur in the Bay of Fundy on the Atlantic Coast of Canada. At Hopewell Cape the water depth at low tide is about 2.0 m and at high tide it is about 12.0 m. The natural period of oscillation is a little more than 12 hours and on June 30, 2009, high tide occurred at $ 6:45 AM. $ This helps explain the following model for the water depth $ D $ (in meters) as a function of the time $ t $ (in hours after midnight) on that day: $ D(t) = 7 + 5 \cos [0.503(t - 6.75)] $ How fast was the tide rising (or falling) at the following times? (a) 3:00 $ AM $ (b) 6:00 $ AM $ (c) 9:00 $ AM $ (d) Noon
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