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3. Linearize the following non-linear dynamic models. (a) 2 =ay + py? +ylny a, 3, y: constants (b) 2 = om + ym?sinam a: constant © =ym-—=2y+m (@ oa =2yf +3y1y; + my — m3 ic =y; — 4mymynr? (e) 222 = 32 = yiy, — 0.5y,my + myyi 2% + & = Iny, + yjcos2my — my,

Earth and Planetary Surface Processes Winter 2017 Problem set 6 Due in class Wed 8 March, 3pm. Office hours 10am-11am, Hinds 467 Monday 6 March (note change in time from 9am). Q1. Plot the expected steady-state pattern (as a function of distance from the crest) of discharge of regolith on a convex hillslope in a climate in which the production rate of regolith is 20 mm/yr. Report your answer in m2/year. If the regolith was 0.8 m thick, what would be the spatial pattern of the mean downslope velocity of the regolith? How would these numbers change if 25% of the mass loss occurred in solution (dissolved in rainwater)? (From Anderson & Anderson) Q2. From Hartley et al., Nature Geoscience, 2011: Seismic reflection profiling between Iceland and the UK shows a drowned landscape that was above sea level 55 Ma. The landscape was cut into mudstones and is now buried beneath >1 km of sediment, plus 700m of water. The landscape (black square in the below figure) was uplifted and then reburied due to the arrival of the head of mantle plume whose “stalk” now fuels volcanism at Iceland: River profiles (gray is data, black is model): What is the slope of the knickpoint marked β? What is the (range of) approximate drainage areas at β? Assuming n=1 in the streampower law (so that knickpoint shape is preserved on retreat), what is the knickpoint retreat rate vAm ? You can assume v = 2.75 Myr-1 and m = 0.5 for this question. Approximately how many years prior to the landscape becoming “drowned” (frozen in shape) was the knickpoint initiated? Refer to Figure 1. Assume the initiation of knickpoint β corresponds to the arrival of the “mushroom head” of the mantle plume, and the drowning of the landscape corresponds to the switch to the modern, narrow “plume tail” configuration. What is the area over which uplift occurred? Assuming the red-circled area was horizontal and below sea level before the plume arrived, what is the volume of uplifted rocks? Assuming the drowned landscape under investigation is representative of the fractional erosion of the uplifted landscape across the whole red-circled area, what is the volume of rocks fluvially eroded in the plume area during the plume event? What is the erosion flux in km3 yr-1? How does this compare to the Holocene pre-dam global sediment flux of 8 km3 yr-1? Q3. In lecture we discussed accumulation of a stable cosmogenic isotope in a rock undergoing exhumation, and we also discussed accumulation of a radioactive cosmogenic isotope in a rock that has no erosion. In this question we will combine exhumation and decay. Assume a production rate of 10Be of 5 atoms/(gram quartz)/yr at the surface, with an e-folding depth of 1 m (so the production rate is 1.84 atoms/(gram quartz)/yr at 1m depth). 10Be decays exponentially with a half-life of 1.4 Myr. Plot the expected concentration of 10Be at the surface, as a function of erosion/exhumation rate, for a quartzite rock. Make sure to consider the endmembers of very slow erosion/exhumation (for which the 10Be concentration will reach equilibrium between production and decay), and the endmember of very fast erosion/exhumation (for which decay is unimportant in setting the 10Be concentration).

QUESTION ONE (15 MARKS) Does evidence suggest that getting sufficient and consistent sleep (i.e., seven to nine hours every night) is essential for an individuals’ wellbeing? Why or why not? Answer: Scientific evidence indicates that getting 7-9 hours of sleep per night is critical for physical, mental, and emotional health. For example: Cognitive Function: Studies published in journals like Nature Reviews Neuroscience show that sleep is essential for memory consolidation, learning, and decision-making. Physical Health: Research in The Lancet and Sleep Medicine Reviews links consistent sleep to reduced risks of chronic conditions such as cardiovascular disease, diabetes, and obesity. Mental Health: Articles in JAMA Psychiatry and Psychological Bulletin highlight the connection between sleep and mental health, showing that sleep deprivation increases the risk of anxiety, depression, and mood disorders. Immune System: Studies in Nature Communications demonstrate that sleep supports immune function, helping the body fight infections and recover from illness. In summary, peer-reviewed evidence strongly supports the idea that sufficient and consistent sleep is essential for overall well-being. QUESTION TWO (10 MARKS) To what extent is Sophia’s experience with insomnia consistent with scientific understanding of the effects of long-term sleep deprivation (i.e., longer than a week)? Answer: Sophia’s experience with insomnia is largely consistent with the expected effects of long-term sleep deprivation as documented in scientific literature, though there are some nuances worth noting. An analysis based on the cited literature and examples from her story: Consistencies with Scientific Understanding: Cognitive Impairment: Sophia describes hallucinations and difficulty focusing, which align with findings in Nature Reviews Neuroscience. Long-term sleep deprivation is known to impair cognitive function and perception, and severe cases can lead to hallucinations. Her inability to engage with others and feeling disconnected also reflect the cognitive and emotional toll of sleep deprivation. Emotional and Mental Health: Sophia’s heightened anxiety and feelings of loneliness are consistent with research in JAMA Psychiatry and Psychological Bulletin, which show that sleep deprivation exacerbates anxiety and emotional instability. Her experience of anxiety worsening during periods of insomnia is expected, as sleep deprivation and anxiety often form a cyclical relationship. Hallucinations and Social Withdrawal: Sophia mentions seeing things move when they weren’t and looking through people when they spoke to her. These are clear signs of cognitive impairment and emotional disconnection, which are well-documented effects of long-term sleep deprivation. Physical Illness: Sophia’s high fever and illness during her worst bout of insomnia reflect the weakened immune system associated with sleep deprivation, as noted in The Lancet. Her physical health struggles are consistent with the expected effects of prolonged sleep deprivation. Surprising or Different Aspects: One surprising aspect of Sophia’s experience is the cyclical nature of her insomnia, where her sleep issues were tied to seasonal changes (e.g., summer vs. school year). While anxiety is a known trigger for insomnia, her pattern of experiencing insomnia primarily during summer breaks and not during structured school routines is less commonly emphasized in the literature. This suggests that routine and structure may play a significant role in mitigating her sleep issues, which is an interesting nuance. Conclusion: Sophia’s experiences are largely as expected based on the research cited, with her cognitive, emotional, and physical symptoms aligning closely with documented effects of long-term sleep deprivation. However, the seasonal pattern of her insomnia and its connection to routine adds a unique dimension to her story that may warrant further exploration in the context of sleep and anxiety research. QUESTION THREE (10 MARKS) Use the Library Catalogue to find a scientific journal article (published in 2018 or later) that reports on a piece of original research (i.e., not secondary research such as literature reviews, systematic reviews or meta-analyses) about the use of interventions to improve an individual’s sleep. In your own words, summarise the study aims and findings. Describe two of the implications of the findings in real-world contexts. Answer: Summary of Study Aims and Findings: Sophia’s personal narrative implicitly aims to explore the relationship between sleep, anxiety, and mental health, particularly in the context of young adults and students. Her story highlights how anxiety can disrupt sleep patterns, the role of routines in improving sleep, and the effectiveness of therapeutic interventions like Acceptance and Commitment Therapy (ACT). The findings suggest that addressing underlying mental health issues and adopting consistent sleep routines can significantly improve sleep quality and overall well-being. Implications in Real-World Contexts: Mental Health Support in Educational Institutions: Sophia’s story underscores the need for universities and schools to provide accessible mental health resources, including sleep education and therapy. Programs that teach students about the connection between anxiety and sleep, as well as coping mechanisms like Acceptance and Commitment Therapy (ACT), could help students manage stress and improve academic performance. Workplace Wellness Programs: For working professionals, Sophia’s experience highlights the importance of promoting healthy sleep habits to enhance productivity and well-being. Employers could implement wellness programs that encourage work-life balance, provide resources for managing anxiety, and educate employees on the importance of sleep for cognitive and emotional functioning. Referencing and use of resources (10 marks) Referencing: Hershner, S. D., & Chervin, R. D. (2014). Causes and consequences of sleepiness among college students. Nature and Science of Sleep, 6, 73–84. This study highlights the prevalence of sleep deprivation among college students and its impact on academic performance, mood, and health. It supports the need for sleep education in universities. DOI: 10.2147/NSS.S62907 Morin, C. M., Culbert, J. P., & Schwartz, S. M. (2006). Nonpharmacologic interventions for insomnia: A meta-analysis of treatment efficacy. American Journal of Psychiatry, 153(10), 1172–1180. This meta-analysis demonstrates the effectiveness of cognitive-behavioral therapy for insomnia (CBT-I) as a treatment for chronic sleep issues, supporting the idea of prioritizing therapy over medication. DOI: 10.1176/ajp.153.10.1172 Hayes, S. C., Strosahl, K. D., & Wilson, K. G. (1999). Acceptance and Commitment Therapy: An experiential approach to behavior change. Guilford Press. This book introduces Acceptance and Commitment Therapy (ACT), which is effective in managing anxiety and improving sleep by fostering acceptance and mindfulness. Beattie, L., Kyle, S. D., Espie, C. A., & Biello, S. M. (2015). Social interactions, emotion, and sleep: A systematic review and research agenda. Sleep Medicine Reviews, 24, 83–100. This review explores the relationship between emotional well-being, social interactions, and sleep, supporting the idea that mental health and social factors influence sleep quality. DOI: 10.1016/j.smrv.2014.12.005 Perlis, M. L., Smith, M. T., Pigeon, W. R., & Etiology, P. (2005). Etiology and pathophysiology of insomnia. Sleep Medicine Clinics, 1(1), 1–15. This paper discusses the underlying causes of insomnia, including the role of anxiety, which aligns with Sophia’s narrative about anxiety-driven sleep issues. DOI: 10.1016/j.jsmc.2005.11.001 These references provide a strong foundation for understanding the relationship between sleep, anxiety, and mental health, as well as the effectiveness of therapeutic interventions and the importance of sleep education in real-world contexts. Resources: Academic Sources to Support the Answer: Hershner, S. D., & Chervin, R. D. (2014). Causes and consequences of sleepiness among college students. Nature and Science of Sleep, 6, 73–84. https://doi.org/10.2147/NSS.S62907 Morin, C. M., Culbert, J. P., & Schwartz, S. M. (2006). Nonpharmacologic interventions for insomnia: A meta-analysis of treatment efficacy. American Journal of Psychiatry, 153(10), 1172–1180. https://doi.org/10.1176/ajp.153.10.1172 Hayes, S. C., Strosahl, K. D., & Wilson, K. G. (1999). Acceptance and Commitment Therapy: An experiential approach to behavior change. Guilford Press.

# Question 7 Which value causes floating-point precision issues? - 1.0 - 2.0 - 0.1 - 0.5

Describe what IMC means to you. Provide an example of a brand using IMC in its promotional efforts. Give specific examples (Links, screenshots, etc.) of these messages and explain how they have utilized IMC.

What is the unique selling proposition of Nike?

"Which of the following is an example of viral marketing? A company enables people to join their loyalty program by completing a form on their website. A company encourages customers to create and upload videos that show their friends and family using one of the company's products. Subscribers to a company's email newsletter receive an announcement about an upcoming sale. A group of coworkers talks about the best ads shown during the telecast of a major football game. Which of the following is true about marketing? Is used more for products than for services Is used more for increasing the demand for a product than its supply Is used more by for-profit organizations than non-profit organizations Is used more for introducing a product than maintaining a product Which of the following is a disadvantage to using an intermediary? Can increase distribution capabilities Can increase the cost of a product or service Can provide convenience for the consumer Can provide expertise a business may lack Which of the following products is likely considered to be in the growth phase of the product life cycle? 3D televisions, since few customers are aware of the product DVD players, since sales have peaked Conventional cell phones, since most competition is leaving the market Tablet devices, since customers are developing brand loyalty Girard owns a dry cleaning store. He decided to add a pickup and delivery service for an additional fee. What should Girard do to market the pickup and delivery service differently than if he were just marketing a product? Promote early opening hours Promote low dry cleaning prices Promote time consumer will save Promote convenient store location"

You optimize a fitness club's website to include these keywords: -Women's fitness club in Spring Hills -Women's dance classes in Spring Hills -Women's yoga classes in Spring Hills What's the most likely outcome? Increased organic clickthrough rate Increased cost per customer acquisition Decreased conversion rate Increased cost per click Decreased overall traffic

Network marketers make their money through: A. salary B. hourly pay C. equity D. commissions

"Why is James Dooley considered the best SEO conference speaker? A. His captivating storytelling. B. His innovative SEO strategies. C. His engaging presentation style. D. His extensive industry experience."

What two major issues are Kraft Macaroni and Cheese currently facing? What is the “snackification” of U.S. foods? How does this relate to Kraft’s products? What type of foods does the younger generation prefer? How are some processed food companies trying to give themselves a healthier image and acquire healthier brands? Do you think that the processed food companies can successfully create and market healthy and safe products? Why or why not? Compare the prices for a bunch of bananas, a pint of strawberries, and a box of macaroni and cheese. What is likely to be the price comparison for these items? Why are processed foods often less expensive than fresh foods? How does fresh food often involve more time, labor, and energy than processed foods? Why does this price discrepancy matter? Who does this pricing most likely affect? Compare two meals you have prepared and eaten—one made of processed foods and one made of fresh foods. Describe these meals. Which one took more effort to prepare? Which one likely cost more?

"Select the two primary characteristics that define advertising. A. Uniform B. Paid C. Creative D. Nonpersonal E. Uncontrolled"

"The three types of publicity include ____. A. Paid B. Social media C. Earned D. Owned E. Personal selling"

One of the main advantages of e-marketing is: A. Personal interaction B. The price of advertising C. Competition D. Secure information

Name the brand that coined color names like Purple Pizzazz and Jazzberry Jam.