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You are studying the impacts of rising sea levels on an estuary, and are modeling how the salinity of a particular area changes with the tidal cycle. The mixed-tide cycle on this part of the coast has a period of approximately 25 hours, giving the salinity fluctuation of the estuary a similar cycle. Twenty years ago, the salinity was modeled by the function s (t) = 12 sin t) -t) + 15, where t is in 25 25 hours and s (t) is the salinity in parts per million (ppm). But you have determined that the model S (t) = 14 sin (t) cos t ) cos 25 + 17 more closely 25 fits the current data. • Graph both s (t) and S (t) using technology. What do you observe about the two functions? How are they the same? How are they different?

You are studying the impacts of rising sea levels on an estuary, and are modeling how the salinity of a particular area changes with the tidal cycle. The mixed-tide cycle on this part of the coast has a period of approximately 25 hours, giving the salinity fluctuation of the estuary a similar cycle. Twenty years ago, the salinity was modeled by the function s (t) = 12 sin t) -t) + 15, where t is in 25 25 hours and s (t) is the salinity in parts per million (ppm). But you have determined that the model S (t) = 14 sin (t) cos t ) cos 25 + 17 more closely 25 fits the current data. • Graph both s (t) and S (t) using technology. What do you observe about the two functions? How are they the same? How are they different?

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.1: Tables And Trends
Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...
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You are studying the impacts of rising sea levels on an estuary, and are modeling how the salinity of a particular area changes with the tidal cycle. The mixed-tide cycle on this part of the coast has a period of approximately 25 hours, giving the salinity fluctuation of the estuary a similar cycle. Twenty years ago, the salinity was modeled by the function s (t) = 12 sin(t t) cos 25 t) + 15, where t is in 25 hours and s (t) is the salinity in parts per million (ppm). But you have determined that the model S (t) = 14 sin (t) cos (t) + 17 more closely 25 25 fits the current data. Graph both s (t) and S (t) using technology. What do you observe about the two functions? How are they the same? How are they different?
Transcribed Image Text:You are studying the impacts of rising sea levels on an estuary, and are modeling how the salinity of a particular area changes with the tidal cycle. The mixed-tide cycle on this part of the coast has a period of approximately 25 hours, giving the salinity fluctuation of the estuary a similar cycle. Twenty years ago, the salinity was modeled by the function s (t) = 12 sin(t t) cos 25 t) + 15, where t is in 25 hours and s (t) is the salinity in parts per million (ppm). But you have determined that the model S (t) = 14 sin (t) cos (t) + 17 more closely 25 25 fits the current data. Graph both s (t) and S (t) using technology. What do you observe about the two functions? How are they the same? How are they different?
Expert Solution
Given

The salinity of a particular area, twenty years ago, was modeled by the function

st=12sin3π25tcosπ25t+15

where t is in hours and st is the salinity in parts per million ppm.

The salinity model that more closely fits the current data is given by,

St=14sin3π25tcosπ25t+17

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