Im seeking for help on the bullet point that starts with 'What do you notice about the t values for...', I would also appreciate help on the questions below this bullet point. Thank you! 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 salinity is also impacted seasonally by snowmelt increasing river flows, so measurements are often taken in early autumn for this particular area. 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 early autumn salinity was modeled by the function $ s(t) = 12 \sin \left( \frac{3\pi}{25} t \right) \cos \left( \frac{\pi}{25} t \right) + 15 $, where $ t $ is in hours and $ s(t) $ is the salinity in parts per million (ppm). But you have determined that the model $ S(t) = 14 \sin \left( \frac{3\pi}{25} t \right) \cos \left( \frac{\pi}{25} t \right) + 17 $ more closely fits the current data.1. **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?**2. **Find both $ s'(t) $ and $ S'(t) $, describing what differentiation rules you use for each, and showing your process.**3. **Use technology to determine the values of $ t $ for which $ s(t) $ and $ S(t) $ have horizontal tangents. (Focus on the first period of the graphs, so $ t < 25 $.** - What do you notice about the $ t $ values for which the two functions have horizontal tangents? - Use these $ t $ values, and the graphs of the two salinity functions, to determine the highest and lowest salinity for the estuary using the historical model and the current model. - What do you notice? How does this relate to what you are studying?4. **Graph both derivatives using technology and use these to determine the values of $ t $ for which $ s'(t) $ and $ S'(t) $ have horizontal tangents. (Focus on the first period of the

Answered: Image /qna-images/answer/e73fa64e-ca25-4ceb-aa4f-5a6103000cb3.jpg

• Use technology to determine the values of t for which s (t) and S (t) have horizontal tangents. (Focus on the first period of the graphs, so t < 25.) • What do you notice about the t values for which the two functions have horizontal tangents?

• Use technology to determine the values of t for which s (t) and S (t) have horizontal tangents. (Focus on the first period of the graphs, so t < 25.) • What do you notice about the t values for which the two functions have horizontal tangents?

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.8: Fitting Exponential Models To Data

Problem 3TI: Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to...

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Question

Im seeking for help on the bullet point that starts with 'What do you notice about the t values for...', I would also appreciate help on the questions below this bullet point. Thank you!

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 salinity is also impacted seasonally by snowmelt increasing river flows, so measurements are often taken in early autumn for this particular area. 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 early autumn salinity was modeled by the function $ s(t) = 12 \sin \left( \frac{3\pi}{25} t \right) \cos \left( \frac{\pi}{25} t \right) + 15 $, where $ t $ is in hours and $ s(t) $ is the salinity in parts per million (ppm). But you have determined that the model $ S(t) = 14 \sin \left( \frac{3\pi}{25} t \right) \cos \left( \frac{\pi}{25} t \right) + 17 $ more closely fits the current data.

1. **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?**
2. **Find both $ s'(t) $ and $ S'(t) $, describing what differentiation rules you use for each, and showing your process.**
3. **Use technology to determine the values of $ t $ for which $ s(t) $ and $ S(t) $ have horizontal tangents. (Focus on the first period of the graphs, so $ t < 25 $.**
- What do you notice about the $ t $ values for which the two functions have horizontal tangents?
- Use these $ t $ values, and the graphs of the two salinity functions, to determine the highest and lowest salinity for the estuary using the historical model and the current model.
- What do you notice? How does this relate to what you are studying?
4. **Graph both derivatives using technology and use these to determine the values of $ t $ for which $ s'(t) $ and $ S'(t) $ have horizontal tangents. (Focus on the first period of the

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