Student Worksheet, Algebra II Activity

Based on AP* Statistics Problem 6, 1997

You are planning to sell a used 1988 automobile and want to establish an asking price that is competitive with that of other cars of the same make and model that are on the market. A review of newspaper advertisements for used cars yields the following data for 12 different cars of this make and model.

Production Year	1990	1991	1992	1987	1993	1991	1993	1985	1984	1982	1986	1979
Asking Price in $	6000	7700	8800	3400	9800	8400	8900	1500	1600	1400	2000	1000

1. Draw a scatter plot of the data. Remember to scale and label both axes.

2. Because of the apparent curvature of the graph, you decide that an exponential function would be a better model for this data. Write an exponential model for this data. Does the exponential function seem to be a good model for the data? Explain why or why not.

3. Use the exponential function to determine a selling price for your 1988 automobile.

4. Your friend thinks that the data would be better represented by using two line segments. Write a piecewise function for the data using two lines or segments of lines.

5. Use your piecewise defined function to determine a selling price for your 1988 automobile.

6. A friend bought a new car last year and he decides to sell it now. Use your exponential model and your piecewise model to predict the price of this car. Which of the two prices would be the most accurate and why?

7. Based on your answer to questions 2-6, decide which model, exponential or piecewise, is a better mathematical model for this situation. Explain why you chose this model.