I have a calculus assignment which I need done. All the instructions are attached in the files selected. This is a part research, part mathematics problem. Thanks!
MCV4U: Calculus: Culminating Assignment Draft Name: ____________________________ In the 1920’s, a scientist (J.P. Maxfield) at Bell Laboratory did research to determine the most optimal design for recording music on a vinyl disk. In 1948, RCA Victor released a new style of record that competed well against those developed by CBS and Columbia. RCA’s new record eventually became the dominate medium for releasing new singles and may still be found today in jukeboxes all across the world. For your final assignment, you will incorporate what you have learned in the Calculus component of the course into a creative presentation. Objective: Create a project that demonstrates a thorough understanding of one particular aspect of Calculus. Ideally, this project will EXTEND the knowledge you have acquired during the course. Format: The format of this project is flexible; choose a format that best allows you to demonstrate your understanding of your chosen topic. Options include (but are not limited to): • Written report with graphs and diagrams • Visual and/or audio presentation (Powerpoint slides, video, etc.) • Creation of physical models with supporting written work Topics covered in class: • Rates of Change • Limits • Continuity • Derivatives • Higher Order Derivatives • Optimization MCV4U Assignment 2021 https://www.google.ca/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=2ahUKEwj5zKbnoefaAhWHz4MKHXAAAjwQjRx6BAgBEAU&url=https://www.pinterest.com/pin/39336196717770581/&psig=AOvVaw2QEirUTms1VlMWfm9MxIuA&ust=1525358574886688 https://www.google.ca/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=2ahUKEwix-66poufaAhXo34MKHfElA-EQjRx6BAgBEAU&url=https://londonjazzcollector.wordpress.com/record-labels-guide/rca/the-rca-labels/&psig=AOvVaw2QEirUTms1VlMWfm9MxIuA&ust=1525358574886688 Project Ideas: Where is the Math? Research a topic that connects Calculus to one or more of the following: technology, art, music, nature, economics or sports. Clearly identify the connection to what you have learned in class, providing ACTUAL examples. Letter to the Editor Write and answer a fake letter to the Editor of Calculus Times from a businessman, a politician or a scientist that poses a simple problem for which you need the use of Calculus to solve. The problem should be detailed and involved. The answer MUST utilize the skills you have learned in this course. Optimize Me! Optimize a 3-dimensional container. Pick a container in the shape of something NOT covered in class. Your container should only have two measurements since you want to have two variables. You can choose to maximize the container’s volume or minimize its surface area. If possible, use a REAL container and include a picture of it with your project. Real Data Function Modelling Using REAL DATA, analyze some sort of a phenomenon. Tell me something interesting about this phenomenon in terms of functions, their derivatives, etc. • Spread of a real disease such as Covid-19, Malaria, AIDS etc. • Record for a specific event in the sporting world • Rate of oil consumption or production • Life expectancies in different countries My Look-Fors: ✓ Topic: the topic chosen is about the application of Calculus ✓ Background: background on the topic is included ✓ Visual Aid(s): shows time, effort, and creativity ✓ Mathematics: the mathematics in the topic is connected to course work; clearly explained, including real examples of the mathematics studied in class ✓ Complexity & expertise: demonstration that something old was consolidated or something new was learned ✓ Organization: organized, clear, and neat ✓ References: Any references that are used in the completion of your project must be cited using APA format. Include references somewhere near the end of your project/report. For help with APA format, consult the website http://www.citationmachine.net/ and click on the “APA” button at the top of the page. This website works for any type of source material: book, magazine, newspaper, journal, web site, etc. http://www.citationmachine.net/ MCV4U – Culminating Assignment Rubric - Draft Criteria Level 4 (Excellent Work) Level 3 (Good work) Level 2 (Satisfactory work) Level 1 (Could be better) Overall Quality Report is of excellent quality, highly creative, interesting, and visibly appealing. Report is of good quality, somewhat creative, interesting and visibly appealing. Report is of satisfactory quality, not very creative, interesting or visibly appealing. Report is of poor quality and lacking in creativity, interest and visible appeal. Application of Mathematics The mathematics in the report is clearly evident and reference to course work is demonstrated and explained. The report is correct and shows significant insight. The mathematics in the report is somewhat evident and reference to course work is mostly demonstrated and explained. The majority of the report is correct. The mathematics in the report is evident but very little reference to course work is demonstrated or explained. The mathematics in the report is trivial and not explained. No reference or connection to course work is evident. Readability Report has few or no errors in spelling, punctuation, and/or grammar. Report is easy to read. All sources are cited. Report has some errors in spelling, punctuation, and/or grammar. Report is readable. Most sources are cited. Report has many errors in spelling, punctuation, and/or grammar. Report is challenging to read. Few sources are cited. Report is unreadable. Sources are not cited. Complexity & Depth of Understanding Report shows excellent depth of understanding of relevant concepts and principles. Report shows proficient depth of understanding of relevant mathematical concepts and principles. Report shows satisfactory depth of understanding of relevant mathematical concepts and principles. Report shows limited depth of understanding of relevant mathematical concepts and principles. MCV4U Assignment Rubric 2021 MCV4U-01 Culminating Task Biological Applications of Calculus in Real Life Calculating Drug Sensitivity: • One of the practices in medical field include measuring drug sensitivity • It is important for doctors and nurses to understand the characteristics of certain drugs that are being prescribed to patients • It is also crucial to know how well the drug will be absorbed into the bloodstream and how long it will remain active in the body • All of these can be measured by comparing the strength of a drug to a patient’s sensitivity to the drug • *The drug strength for a certain drug is not applied for all drugs • The strength of the drug is usually given by R(M) • M measures the dosage in milligram (mg) For example: ?(?) = ??√?? + ?. ?? We can use the product rule and the chain rule to find the derivative. • The derivative of the function represents the sensitivity of the patient’s body to the drug Assume the drug strength, with a dosage of 325mg, is being calculated The derivative calculated to be ?′(?) = 3?+40 √2?+40 Substitute 325 mg into M ?′(325) = 3(325)+40 √2(325)+40 • The sensitivity of a patient's body to the drug with a dosage of 325mg is about 38.64. The graph ?(?) = 2?√10 + 0.5? represents the strength of a certain drug. The derivative of the drug equation, ?′(?) = 3?+40 √2?+40 , represents the sensitivity of patient’s body to the drug. By comparing the two graphs, it can be seen that the drug strength has changed By applying the derivative, drug sensitivity for a patient can be accounted for By knowing the drug sensitivity of a patient to certain drugs with respect to the dosage, doctors and pharmacists are able to test the effects that it will have on the body Therefore, the drug will be able to work more effectively. Example: Calculating Drug Sensitivity in Real Life using Optimization • The sensitivity corresponds to approximately how much change to expect in R as the result of a unit change in the dosage. • Generally, doctors prefer to prescribe dosages of maximum sensitivity. • The strength of a patient’s reaction to a dose of M milligrams of a certain drug is R(x) = ?1? 2(?2 − ?) where c1 and c2 are positive constants. For what value of M is the strength a maximum, and what is that maximum reaction value? For what value of M is the sensitivity a maximum? What is the maximum sensitivity? Environmental Application of Calculus in Real Life In the field of chemistry, calculus can be used to predict functions such as reaction rates and radioactive decay. We can use the following equation to calculate the average rate of reaction of a reactant product, A: ????? = ?????????????? ?? ? ?? ???? ?2 − ????????????? ?? ? ?? ???? ?1 ?2 − ?1 Or ????? = ∆[?] ∆? • The chemical symbol (A) placed inside the square brackets indicate the entity’s concentration in mol/L. For the decomposition reaction of nitrogen dioxide, NO2(g), a brown gas that can be formed from gasses in tailpipe emissions. It is a major component of smog. The ground-level NO2(g) and one of the products of its decomposition, NO(g), undergo further reactions that increases ground-level ozone, which harms humans and other living things. We can calculate the average rate at which the NO2(g) is consumed over the first 50 s of the decomposition reaction. ????NO2(g) = ∆[NO2(g)] ∆? = [NO2(g)]?=50? − [NO2(g)]?=0? 50 ? − 0 ? = 0.0079 ??? ? − 0.0100 ??? ? 50 ? ????NO2(g) = −4.2 × 10 −5 ???/? ∙ ? We can also calculate the average rate for the disappearance of NO2(g) for each 50 s interval. Over the same period the rate of oxygen production is given by ????O2(g) = + ∆[O2(g)] ∆? = 2.2 × 10−5 ???/? ∙ ? Environmental engineers can use the results from the average rate of reaction and engineering principles to solve environmental problems, such as the decomposition of NO2(g). Example: Calculating Carbon Monoxide Level using the Chain Rule An environmental study of a certain community suggests that the average daily level