Spring Semester Honors Project

The purpose of this project is to collect different types of data, graph them, and model them with mathematical equations that can be used to analyze and make predictions. You will graph, model, and analyze 3 types of data: linear, quadratic, and exponential.

Linear Functions:

A. Go to the website , find the title “Sports” and select “Track and Field.” Scroll down to select the 400m Men data. This page will display the results of the men’s 400 meter run from 1896 through 2004. We only want the gold medal times. Enter the years in L1, let x=0 correspond to 1900 (careful – these do not always increase by 4). Enter the gold medal times in L2.

  1. Create the scatterplot of the year vs. gold medal time.
  2. Calculate the line of best fit.
  3. Use the equation to predict the gold medal time for the 2008 Olympic Games.
  4. What was the 2008 gold medal time for the 400m event and how does your prediction compare?
  5. We modeled this data with a linear regression;find the exponential equation for the data.
  6. Which regression equation would best model future races? Why?

B.There has been a lot of discussion over global warming over the last several years. The warming trend is blamed on an exponential growth of CO2 gasses, which we will model in the exponential section of the project. Many people believe that the average global temperature is increasing exponentially as well. Let’s look at the average global temperatures from the website Scroll down to find the Table of Average Global Temperature by Decade from 1880 to 2004. To make our equation easier to work with we need to make 1880-1889 be decade 0. Enter the decades in L1 and the temperature in L2

  1. Create a scatterplot of the decadessince 1880-1889 and Average Global Temperature.
  2. Fit a linear equation to the data.
  3. Use the equation to predict the average global temperature in 2010-2020.
  4. Fit an exponential equation to the data.
  5. Does it appear that the temperature increase over the last 100 years is linear or exponential? Explain your response.
  6. Read the 7th paragraph, that begins “Try another case…”, from an article quoted from by John H. Lienhard from The University of Houston's College of Engineering. How does this excerpt confirm or deny your response to problem #5?

Quadratic Functions:

C.Go to the website and scroll down to find the data for speed vs. stopping distance. We will be modeling the speed vs. total stopping distance data, so you can ignore the middle three columns.

  1. Create the scatterplot of the speed vs. total stopping distance
  2. Calculate the best-fit quadratic equation for the data.
  3. Use the equation to predict the stopping distance for a car traveling at 72 mph.
  4. Use the equation as a police officer would: if the skid marks were 200 ft long how much over the 35 mph speed limit was the driver going? Explain how you got your answer.

Exponential Functions:

D. Much discussion has taken place over the exponential increase in CO2 emissions and global temperature over the last century. Let’s analyze that idea. The website gives the CO2 emissions for the last 200 years. The average CO2 emissions for the decades from 1880-2005 are provided in the table.

1880-1889 / 278.9 / 1950-1959 / 2018.3
1890-1899 / 409.2 / 1960-1969 / 3097.6
1900-1909 / 658.2 / 1970-1979 / 4700.4
1910-1919 / 876.3 / 1980-1989 / 5488.7
1920-1929 / 974.3 / 1990-1999 / 6371.3
1930-1939 / 1040.6 / 2000-2005 / 7270.5
1940-1949 / 1342.7

Again, let x=0 correspond to 1880-1890.

  1. Create a scatterplot of the data
  2. Fit an exponential equation to the data.
  3. Use the equation to predict the amount of CO2 emission in the year 2010-2020.
  4. What is CO2 emission?
  5. Write a paragraph about the significance of the global temperature data in part B and this data in part D.

E. You will probably be attending college within the next few years. The cost of that college education is increasing each year. The following table gives the annual tuition and fees for the University of North Carolina at Chapel Hill from 1985 to 2009.

YEAR / TUITION & FEES
2009 / 5626.00
2008 / 5487.00
2007 / 5339.58
2006 / 5033.08
2005 / 4613.02
2004 / 4450.52
2003 / 4072.04
2002 / 3856.1
2001 / 3277.42
2000 / 2768.32
1999 / 2365
1998 / 2262
1997 / 2224
1996 / 2161
1995 / 1686
1994 / 1569.42
1993 / 1454
1992 / 1284
1991 / 1248
1990 / 1084
1989 / 1008
1988 / 876
1987 / 845
1986 / 819
1985 / 794

Data collected from

  1. Copy this table into a stat list and adjust the years so that 1985 is 0 as in the other data sets.
  2. Create a scatter plot of the data.
  3. Fit a linear equation to the data.
  4. Fit an exponential equation to the data.
  5. Use both equations to predict the 2010 tuition and fees at Carolina.
  6. Which tuition prediction to you think is a more reasonable estimate of the cost of attending Carolinain 2010?

F. Find a data set that can be modeled by a function that we have learned in Algebra 2 this year. Provide a copy of this data that you found on the web, newspaper, magazine, or that you collected.

1. Find the regression model that best fits your data.

2. Explain your choice.

3. Make a prediction for an extension of your data.

Data Analysis Project Answer Sheet

A. 2. Linear Equation ______

3. Prediction ______

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4. Time ______

______

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5. Exponential Equation ______

6. ______

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B. 2. Linear Equation ______

3. Prediction ______

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4. Exponential Equation ______

5. ______

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6. ______

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C. 2. Quadratic Equation ______

3. Prediction ______

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4. ______

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D. 2. Exponential Equation ______

3. Prediction ______

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4. ______

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5. ______

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E. 3. Linear Equation ______

4. Exponential Equation ______

5. 1st Prediction ______

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2nd Prediction ______

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6. ______

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F. Copy of Data Provided ______

  1. Regression Equation ______

2. ______

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______

3. Prediction ______

______

Grading Rubric:

The project will be graded on a 100 point scale.

To receive an “A” all responses are complete, accurate, and thoughtful.

An omission of an analysis of any data set will automatically drop you a letter grade.