Math 1101 - Project



Math 1101 – Project 1

This project is due on 13 October 2003 (tentative). You may complete the project in a group of two to four students. Normally, all members of the group will receive the same grade; however, the instructor reserves the right to conduct individual interviews over the content of the project and to assign different grades to different members of the group.

Introduction and Data

In recent years, the season homerun record has fallen twice (first Mark McGwire hit 70 homeruns in 1998, then Barry Bonds hit 73 in 2001). Will the career homerun record fall (this is held by Hank Aaron who hit 755 in his career)? You will be making a projection of the career homerun totals for the four baseball players below (you may include other additional players). Note: if your interest is not baseball, then you may find (subject to the instructor’s approval) another data set that you can use for the project. The instructor and the students will devise the questions to answer. This data set must be determined prior to 29 September 2003.

|Year |Barry Bonds |Ken Griffey, Jr. |Alex Rodriguez |Sammy Sosa |

|1 |16 |16 |0 |1 |

|2 |41 |38 |5 |8 |

|3 |65 |60 |41 |23 |

|4 |84 |87 |64 |33 |

|5 |117 |132 |106 |78 |

|6 |142 |172 |148 |86 |

|7 |176 |189 |189 |119 |

|8 |222 |238 |241 |144 |

|9 |259 |294 |298 |180 |

|10 |292 |350 |338 |220 |

|11 |334 |398 | |256 |

|12 |374 |438 | |322 |

|13 |411 |460 | |385 |

|14 |445 |468 | |435 |

|15 |494 |481 | |499 |

|16 |567 | | |531 |

|17 |613 | | | |

|18 |653 | | | |

*data is accurate to 4 September 2003.

Questions

You are asked to make projections, based on the above data, about two questions. Note there may be more than one correct answer. Please support your conclusions.

▪ Question 1: How many career homeruns will each player have after 20 years?

▪ Question 2: In which season will the player hit his 756th homerun?

Methodology

You will develop three different models (described below) for the data. In each model, let x denote the number of years the player has been in the major leagues and let y denote the number of homeruns. For example, [pic]would refer to fourth season that Barry Bonds was in the majors and [pic] is the number of homeruns he hit through the first four seasons.

You should use each of the three models to address the two questions described earlier.

▪ Model 1: A linear model of the form [pic].

▪ Model 2: An exponential model of the form [pic].

▪ Model 3: A quadratic model of the form [pic].

The regression features of your calculator are capable of performing linear, exponential, and quadratic regression using, respectively, the LinReg, ExpReg, and QuadReg commands in the [Stat] [Calc] menu.

Final Report

You are to present a written report describing your findings. Include the following items

▪ An introduction summarizing the information provided to you.

▪ An analysis section in which you clearly show the equation you find for each of the three models and the mathematical work involved in answering the two questions with each of the three models.

▪ A conclusion that summarizes your findings, including other data as necessary.

Please follow these guidelines when preparing your report:

▪ Papers should include a mixture of tables, graphs, equations, and written explanations. Your textbook can serve as a model. For example, look at the equations, tables, and graphs in your textbook and notice the way the text inserts these into the flow of its written explanations. In particular, note that an equation is usually easier to read if centered on a line by itself.

▪ Papers should be typed. You may write equations and formulas in by hand or you can use the built-in equation editor in Microsoft Word. Click on Insert on the command bar, select Object, and select Microsoft Equation. If you use Microsoft Word at home, you may need to install this feature. Use the built-in help feature to look for instructions to "install or remove individual components".

▪ Graphs from your calculator may be printed or copied into a word processor using TI-Graph Link software. This software is available in the ISS lab.

▪ Tables and graphs can be made and printed or copied into a word processor using Excel software, which is also available in the ISS lab.

▪ Clearly explain your reasoning. Focus on explaining what you are doing conceptually, not on the mechanics of the algebra. You may assume that the intended reader has a working understanding of the mathematics.

▪ You are not writing a user's manual on how to use the calculator. Do not write about which keys you pressed on your calculator.

▪ Turn in one paper per group. The instructor will keep all papers. Make a copy for your files before turning in your paper.

You will be graded on the quality and clarity of your written presentation as well as the mathematical accuracy of your paper.

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