MATH-143 - Precalculus I Project #2: Making a Rational Decision 42 points To be successful on your project you must: Read and follow instructions carefully. Review the grading rubric carefully to ensure you are familiar with the expectations for each section. If you need clarification about any part of this project, please be sure you ask your instructor in a timely manner. o Ten percent will be deducted for each calendar day the project is submitted after the due date. A project is considered as \"submitted\" when it is available to the professor to view in Canvas. No credit is given after five days late (2 calendar days during winter/summer terms). o After you submit your project please open it up in Canvas to ensure it is readable. Write clearly, using appropriate terminology and accurate mathematical notation. College-level writing is expected, as is the use of correct grammar. o If you need help with writing, feel free to use the HCC Writing Center: For further information, see the HCC Web page under the heading \"Writing Center\" or call the Writing Center at (443) 518-4101. PGCC students at the Laurel College Center should see the PGCC Writing Center for assistance. Submit a neat, professional report typed (double-spaced) using your choice of word processing software (including a mathematical notation package) and including printouts and diagrams from your choice of graphing application, computer algebra software, or statistical software (as applicable). The use of appropriate technology is expected throughout the project. o In particular, embedded \"complete\" graphs or charts and/or computer printouts will be expected as part of the report. Hand-drawn graphs are not acceptable. o Hand calculations (if applicable to the project requirements) should be scanned and included as an appendix at the end of the report. For this project group work will not be allowed. While you may get ideas from others, each student must submit their own project. Original work is expected. This means that students who are repeating the course are expected to create an entirely new project using different functions. Getting help: You may ask questions of others but your work must be your own and you must write up your own documents to be turned in. o For this project, you may consult any resource (including your instructor, tutors (LAC, HR230), classmates, or the Internet) for general help and advice provided that your writeup (computations, explanations, and embedded diagrams) are your own work. o For example, you might watch a YouTube video on how to do a regression or have a peer show you how to make a complete graph using a different dataset (not the one in your project), then try it yourself with your data. You might consult your textbook or your instructor about a concept, but then put the explanation into your own words. Submission guidelines: o You should submit your project via the Canvas link as a Microsoft Word or PDF file. o TurnItIn will be used as a deterrent to plagiarism. This program is integrated into the Canvas submission process. All submissions will be compared against the TurnItIn database and receive an \"originality\" rating. To avoid a false flag in TurnItIn, do not copy and paste the instructions/questions into your final submission. o To earn the maximum score on this project, it is expected that students go \"above and beyond\" the minimum expectations of the project. MATH-143 - Precalculus I Project #2: Making a Rational Decision 42 points Any new electrical device, such as a refrigerator, washing machine, computer, stove, air conditioner, or hot water heater, will cost more over time than just its purchase price. The cost of energy to run the appliance is an important component of the total cost. Many appliances now meet the requirements to be called \"Energy Star\". In this activity you will select any electronic device with an \"Energy Star\" rating. You will need the cost of the device (which might change after you select your device) and you will need the estimated yearly energy cost. This information will allow you to construct a rational function that describes the average cost of owning and operating the device over a period of time (ignoring other costs). Information can be found many places, including on the web, in an ad, or in a store. Example images: (NO, you may not use the device in this example; YES, you may use any other device at this web site) Device: Dryer, link: http://www.bestbuy.com/site/lg-4-0-cu-ft-7-cycle-ultralarge-capacity-high-efficiencyfront-loading-washer-white/1713767.p;jsessionid=FDC7507D3ADF11C7C5375E83919E2B37.bbolsp-app04191?id=1219061247609&skuId=1713767&st=select-washers-and-dryers-128910&cp=1&lp=4 Buying Price: $629.99 (as of 10/5/2014) Energy Star Cost link: http://pisces.bbystatic.com/image2/BestBuy_US/images/products/1713/1713767_eg.jpg;canvasHeight=500;can vasWidth=500 MATH-143 - Precalculus I Project #2: Making a Rational Decision 42 points For this project you are expected to do the following: Find any Energy Star device (you do not need to actually purchase the device). Some places where you can find them are paper ads, online ads, or by going into a store and finding one. Post your photo to the Project Discussion on your course Canvas site. You may not select a photo already used by one of your classmates. Each student will need a different image. Be sure to include at least the following information in your post: o The type of device o The cost of the device o The annual energy cost to run the device o One of the following: One or more links to web sites where you found the device, cost, and energy cost; OR Your photo(s) of the device, cost, and energy cost Write a report about your results. You must discuss/inlude at least the following: o A digital image of the appliance and the Energy Star Energy Guide, with an appropriate citation o Answers to the questions below. Use technology to do the following. The total cost of your device, in dollars, C t , depends on three quantities: C0 , the initial cost of the device (does not change with time); , the annual energy cost of the device (does not change with m time); and , the time since the device was purchased (the independent variable for the problem). You t are to ignore all other costs of operating your device, such as repairs or replaceable components. o Write a symbolic formula for in terms of the variables , , and . t C0 m C t o Write a function , replacing C t The average cost, in dollars per year, C0 and m with the values for your device. , will turn out to be the total cost divided by . is a t AC t AC t rational function. Write the rational function representing the average cost function per year for your device. Write the domain of if you don't consider the context of the problem. This is called the natural AC t domain of the function. For this application, the domain for the average cost function has to be restricted. Write the restricted domain for AC t . Use technology to make a complete graph of your average cost function. There is a description of what is required for a complete graph in your objective packet. Be sure to graph only the interval of the natural domain that makes sense in the context of this project (the restricted domain). Graph the horizontal asymptote for your average cost function. Another company offers to sell an alternate to your device for 25% more than the cost of your device. The annual energy cost of the alternate device is half of the annual energy cost for your device. For MATH-143 - Precalculus I Project #2: Making a Rational Decision 42 points example, if your device costs $10 per year for electricity, if the alternate device costs 50% of that it will cost $5 per year for electricity. Write the rational function that represents the average cost per year for this alternate device. Use technology to make a second complete graph showing both functions and any intersection point(s). Questions to answer: Why does the domain of AC t need to be restricted, and what values of the natural domain are not reasonable? Explain the meaning of the horizontal asymptote in the context of this problem. What is the significance of any point(s) of intersection in the context of this problem? Which device represents the better value if you keep the device for 1 year? 5 years? 20 years? Why did you select the device you did? What technology did you use in this project? For each type of technology, explain why you chose it. What difficulties did you encounter? What would you do differently next time? Write what you would communicate to someone else about the usefulness of comparing the average cost of different devices (remember to cite your sources). Grading Rubric (42 points possible): Digital image, 5 points total 1: Image of device and costs 1: Posted to Canvas Web Site 1: Post includes link to image, or statement taken by self 1 Included in report (can be part of the final image) 1 Correctly cited in report Three Equations, 6 points total 2: Formula for 2: Function 2: Average cost function C t C t for your device AC t for your device Restricted Domain, 2 points 1: Natural domain 1: Restricted domain Alternative device average cost function, 4 points 1: Correct initial cost for alternate device MATH-143 - Precalculus I Project #2: Making a Rational Decision 1: Correct cost per year for alternate device 2: Average cost function AC(t) for the alternate device Graph, your device, 5 points 1: Use appropriate technology 1: Horizontal axis with label and appropriate units 1: Vertical axis with label and appropriate units 1: Graph AC(t) for your device 1: Graph horizontal asymptote for your device Graph, alternate device, 5 points 1: Graph AC(t) for alternate device 1: Horizontal axis with label and appropriate units 1: Vertical axis with label and appropriate units 1: Graph point(s) of intersection 1: Label point(s) of intersection Questions, 10 points Document, 5 points 1: Double spaced 1: Microsoft Word or PDF document 1: No more than three minor grammatical errors 1: Mathematical notation correctly implemented 1: Directions and questions not included Total Points: 42 42 points MATH-143 - Precalculus I Project #2: Making a Rational Decision 42 points Gen Ed Assessment Rubric (Not part of the grade) Technology Considerations TC Criterion #1: Identifying appropriate technologies to efficiently complete tasks, solve problems, create new works or improve processes across a variety of disciplines 4 Points Identifies effective and efficient technologies for the needed tasks. 3 Points Identifies effective and efficient technologies for needed tasks. Indepth analysis and justification of technology choice included. Technology choice not thoroughly analyzed and/or justified. 2 Point Identifies technologies which are not effective and not the most efficient for the needed tasks. 1 Points Does not identify appropriate technology for given task or the selected technology cannot perform the required task. 0 Points No submission, submission is plagiarized, or submission does not match assignment. Effective Use of Technology TC Criterion #2: Using, adapting or designing technologies to achieve the best results for research, communication or taskrelated objectives 4 Points Multiple, complementar y technologies utilized to yield outstanding results, demonstrating advanced command of each of the tools. 3 Points Multiple technologies used appropriately to complete project tasks in a manner sufficient to meet project goals, demonstrating proficiency in utilizing multiple tools. 2 Points Project utilizes some technology, but does not completely or consistently meet project goals. 1 Point No technology used. 0 Points No submission, submission is plagiarized, or submission does not match assignment