Directions

This problem is to be completed in your group. Your group should hand in one copy of the assignment, for which each group member will receive the same grade. There will be about six projects during the semester. Each group member must be responsible for writing up the final report for at least one of the assignments.

The project report should have three sections. Naturally, if a section is missing, it will receive zero points. That means a correct solution alone, without the other parts, is worth at most four out of ten points!

Part 1. (3 points)

Give a general description of the problem, including what is problematic about the exercise. This should not just be a restatement of the problem. Instead, you need to show that you understand the main idea of what you are trying to do. You don't need to give all the details, just the big picture, in your own words. You do not say anything here about how you solved or attempted to solve the problem-that comes in the next part. This should take a paragraph (more than a sentence, less than a page).

Part 2. (3 points)

Describe how your group tackled the problem. In this part you describe what you tried, including both things that worked and false starts that were not productive. This is a description of your strategies, not a blow-by-blow listing of every thought that occurred to you. You should not actually give your solution here, not should any of the work supporting your solution appear in this part. Again, this will take more than a sentence or two, but a page is probably more than enough.

Part 3. (4 points)

Your solution should be accurate, carefully written, and concise (to the point). In each part you need to write your responses using sentences. This is something you may not have done in the past when writing a solution to a mathematical problem, so be sure to do so now!

You may work on these projects only with members of your group. Obviously, not everyone can come up with the solution, but everyone is expected to contribute by working hard and discussing their thoughts. You must include this statement at the end of your report:

We have neither requested nor received any help from individuals outside our group on this problem. Each of us has contributed to the work on this problem, and we will not allow anyone to sign this paper who has not contributed in some way.

All members must attest the truth of the statement by signing the paper that they turn in. You should discuss any problems about your group work with your instructor.

Project 1

Part 1 of Project 1. Introduction to Curve Fitting.

This project involves ideas that are discussed on pages 103-111 in your text. We will introduce the ideas with an exercise that asks you to plot points and linear functions using a graphing calculator. This will be a good review of important material that you studied in previous mathematics courses.

Complete problem 1(a) on page 108 using your calculator to plot the points. Then find equations for three lines that appear to fit the plotted points well (HINT: you should be able to find the equation of a line through any two points, which might help you get started). When you have found first line, think about adjustments of slope and position that could improve the fit of the line to the data.

Once you have three different lines that fit the data well, decide which is the best fit. Be sure to explain how you decided. You will be asked to share your group's choice with the class. Then answer 1(c) on page 108. (This portion of the project will be completed in class)

Part 2 of Project 1. Linear and Exponential Regression.

Your calculator can find and plot regression lines for data. The user manual can help you do this (the method varies for different calculator models, but it is not very complicated). Find and plot the regression line for the first data set (above). Comment on how your best line of fit compared with the calculator's regression line.

Now complete problem 7 on page 109. Your calculator's user manual will tell you how to fit an exponential equation to data points (this is called exponential regression-fitting a straight line is called linear regression).

Part 3 of Project 1. Polynomial Curve Fitting.

Answer problem 11 (page 110). Then estimate the coordinates of 10 points on the graph, plot them on your calculator, and try to fit a polynomial to the points.

Describe how well your polynomial fit the points-be sure to give the equation and the points that you used.

Part 4 of Project 1. Conclusion

Answer Problem 12 (page 111).

Then describe what it means to fit curves to data and explain why this is useful.