calculus

PRO J E CT I

MTH 151, SU MME R 2021

Derivatives

Due: October 28, 2021

Work in groups of two or three on this assignment. The report must be typed and well organized. It must be written in complete sentences and all the argu- ments must be justified. The report can not exceed three pages. This assignment will be graded both for mathematical quality and expository quality. The textbook provides good models of mathematical expository style. The handout Writing in Mathematics (available on canvas) provide additional advice. In particular,

• Write the paper for an audience of advance algebra students.

• Begin your paper with a brief introduction. You should restate the prob- lem in your own words and as you understand it.

• Shows mastery of the meaning of the functions and their properties.

• Is mathematically correct as well as grammatically correct.

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• Is well organized, coherent, and well written.

• Explain why you included the mathematical calculations or graphing method you did.

• Mix necessary mathematical equations and expressions with sentences of logic and explanation.

• Use present tense in explanations. Use ‘we’ to indicate the reader and author working together to solve the problem.

• Graphs and tables can be helpful. Any graph and/or table needs to be clearly labeled (both axes and key points) and the text needs to refer to it and explain what it shows.

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The graphs on the Figure 0.1 show yearly mean carbon dioxide measured at Mauna Loa Observatory, Hawaii. https://gml.noaa.gov/ccgg/trends/data. html Answer the following questions using the fitted curve given by following function

y = 310.47839973172 + 0.51399610965x + 0.01358176339x 2

that is represented in Figure 0.1.

1. According to the model what will C O2 levels be in 2050?

2. What is the rate of change of C O2 in 2019 (the last year of the data set) and what is the percentage rate of change?

3. Assuming that C O2 levels continue to grow constantly at the 2019 rates, what will the CO2 levels reach in 2050? Compare your solution the the answer to question numer 1.

4. Atmospheric C O2 levels of 450ppm yield a likely chance that global av- erage temperature increases will be at least 20 Celsius1. According to the model, in what year do we reach a C O2 level of 450ppm? If we assume C O2 levels continue to grow constantly at the 2018 rates, in what year do we reach a CO2 level of 450ppm?

5. In conclusion summarize your work on questions to a short paragraph(s).

1According to IPCC Fifth Assessment Report (AR5) page 22: https://www.ipcc.ch/pdf/ assessment-report/ar5/syr/AR5_SYR_FINAL_SPM.pdf

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Figure 0.1: plane

GR AD I N G RU BR I C

Mathematical content (30%) Is the mathematics consistent and correct? Is it at a level of sophistication appropriate for this class? Are topics and ideas introduced with sufficient explanation? If there are pictures, figures or examples, are they accurate, appropriately used and do they support the text?

Clarity of mathematical exposition (30%) Are topics presented in a log- ical order? Does the paper achieve an appropriate balance of concise- ness and explanation? Are complicated parts/proofs (if any) broken into steps?

Style (40%) Is the paper clearly written, in paragraph form? Is the gram- mar, spelling, and sentence construction correct? Does the introduction serve its purpose? Is the paper readable, does it flow?

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