Explanation Given information: 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 2.0m and at high tide it is about 12.0 m. the natural period of oscillation is about 12 hours and on June 30, 2009, high tide occurred at 6:45 AM. Calculation: Given that high tide occurred at 6:45 AM means 6 hours 45 minutes = 6 hrs 45 min 60 min = 6.75 hr . For standard cosine function, the following equation is Y = A ↓ cos [ B ( x − c ) ] + D ↑ Amplitude midline Taking an average of high and low tides 12 + 2 2 = 14 2 = 7 So the value of midline is, D =7 Next we will find amplitude. Now the amplitude is simply measure from the midline to either the highest value or the lowest value like 12 − 7 = 5 or 7 − 2 = 5 So, A = 5 M=next we find the value of c c is simply the x-coordinate of where our curve begins its cycle

Bundle: Biocalculus: Calculus, Probability, And Statistics For The Life Sciences + Webassign Printed Access Card For Stewart/day's Biocalculus: Calculus For Life Sciences, 1st Edition, Multi-term

1st Edition

ISBN: 9781305779037

Author: James Stewart, Troy Day

Publisher: Cengage Learning

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Question

Chapter 1.3, Problem 23E

To determine

To 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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Chapter 1.3, Problem 22E

Chapter 1.3, Problem 24E

Chapter 1 Solutions

Bundle: Biocalculus: Calculus, Probability, And Statistics For The Life Sciences + Webassign Printed Access Card For Stewart/day's Biocalculus: Calculus For Life Sciences, 1st Edition, Multi-term

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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.

Solution Summary: The author explains the cosine function that models the water depth as a function of time t (in hours after midnight).

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To 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.

Want to see the full answer?

Chapter 1 Solutions