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To be mathematically literate it is imperative that you be able to effectively communicate mathematical concepts in a written fashion using correct mathematical notation. This assignment is one step in helping you become more mathematically literate.
We have learned how to find exponential models from word problems as well as graphs. We have seen that all these exponential models fit into the general form f(x) = P(a)x. However, some folks such as biologist, economist, or other scientist use different forms of this model.
Assignment
You will be given a set of data. With this data you will use your calculator to perform an exponential regression. Most calculators will output this model in the form y = a(b)x. Once you have this model you will then find two different models by modifying the calculator model. One in the form, g(x) = Pekx, and the other h(x) = P(2)x/d.
Your paper will be graded on presentation, completeness, accuracy, and punctuality. It will be graded using the rubric on the back. The rubric must be attached to your paper when submitted. This project is Due Wednesday, Nov. 21st, 2007.
Guidelines
Your paper must be typed or neatly hand-written and fit entirely on one side of one page. Your paper should be mathematically sound and understandable to your audience.
Your paper must clearly describe the regression process in general terms. Although your paper should include some calculator instructions, those instructions should be general in nature and pertain to any brand of calculator. I do NOT want an extensive description of calculator steps. In addition, I want you to explain the mathematical procedure you used to find each model.
There should be at least 4 sections: Introduction, Regression Procedure, Finding other Forms Procedure and Conclusion.
Your paper must include a problem statement (paper's purpose) in your own words in the Introduction so that someone not familiar with the assignment would understand the purpose of the paper. Also, the Introduction should include some human interest to motivate the assignment.
Your paper must contain a scatter plot depicting the data in the table as well as the graph of your model with the scatter plot.
In the Conclusion you will need to contrast the different models. That is, explain to the reader what each model yields from inspection. A good way to think about this is to explain what the letters P, a, k, d represent in the context of this example.
The table to the right gives the population of Deschutes County for several years from 1920 to 2000. Perform an exponential regression on this data to find an exponential model that models this data. Then carefully sketch or a get a calculator screen shot of the scatter plot and the exponential model for this data.
Once you have your model, find two models that also model this data. One in the form, g(x) = Pekx, and the other h(x) = P(2)x/d.Year
Population
1920
9,622
1940
18,631
1960
23,100
1980
62,142
1990
74,958
2000
115,367
Check List
(Neatly written?(Contains a title?(Fits on one page?(Proof read?(Checked spelling?(Checked grammar?(Mom can understand it?(Clear/labeled diagram(s)?(Too much calculator detail?(Used function notation?(Contains a motivator?(Procedure written in general terms?Mth 111 Project NAME
OVERALL FORMAT
Layout: margins, use of white space, placement of information on the page
Organization and presentation: appropriate use of bulleted lists, charts or diagrams, grammar and spelling.
4Typed with clearly readable font or neatly written with title and other clarifying headings. Layout and information organization/presentation flows for easy readability. 3Typed with clearly readable font or neatly written. Layout or information presentation slightly affects readability.2Font type, handwriting or layout affects readability which in turn affects information presentation. 1Readability is significantly hindered by font type, handwriting, layout and/or information presentation.
FOLLOWING GUIDELINES FOR THE PAPER
Paper length, due date, scatter plot and graph, different models explained
4Meets all the guidelines for the paper3Meets all but one of the guidelines for the paper2Meets all but two of the guidelines for the paper1Fails to meet three or more of the guidelines for the paper
CONCEPTUAL UNDERSTANDING
Interpretation and explanation of mathematical concept(s)
4Interpretation and explanation of mathematical concepts is clear and correct.3Interpretation and explanation of mathematical concepts is reasonably clear and mostly correct but suggests possible minor misunderstanding.2Interpretation and explanation of mathematical concepts is somewhat unclear and or partially correct but suggests significant misunderstanding.1Interpretation and explanation of mathematical concepts is so unclear or error prone that it suggests significant misunderstanding.
PROCESSES AND STRATEGIES
Choosing strategies that work, explaining them and applying them to an example
4Processes and/or strategies used to solve the task are clear, correct and lead to a correct solution.3Processes and/or strategies used to solve the task are reasonably clear, correct and lead to a correct solution or a solution with an error not suggestive of a lack of understanding.2Processes and/or strategies used to solve the task are rather unclear and or contain one or more errors indicating a lack of understanding of the problem solution.1Processes and/or strategies used to solve the task are so unclear or contain substantial errors suggesting significant misunderstanding.
COMMENTS AND OVERALL GRADE
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