The United States gross national product in trillions of dollars for the latter half of the 1980s is given in the table below. Year 1985 1986 1987 1988 1989 GNP ($trillion) 4.02 4.23 4.52 4.88 5.20 1. Using technology, calculate the average rate of change for each year. You may, for example, make a table in a spreadsheet with Year, GNP, and Average Rate of Change, as the three columns. What are the independent and dependent variables? 2. Using technology, create a plot of GNP vs year. Does the data appear to be linear? Explain. 3. Using technology, construct a linear trendline and determine the R2 value. What is the trendline equation? Interpret the slope, including units. What is the R2 value? Is there a strong or weak correlation?
The United States gross national product in trillions of dollars for the latter half of the 1980s is given in the table below.
Year 1985 1986 1987 1988 1989
GNP ($trillion) 4.02 4.23 4.52 4.88 5.20
1. Using technology, calculate the average rate of change for each year. You may, for example, make a table in a spreadsheet with Year, GNP, and Average Rate of Change, as the three columns. What are the independent and dependent variables?
2. Using technology, create a plot of GNP vs year. Does the data appear to be linear? Explain.
3. Using technology, construct a linear trendline and determine the R2 value. What is the trendline equation? Interpret the slope, including units. What is the R2 value? Is there a strong or weak correlation?
4. Using the trendline equation, create a spreadsheet table and second plot of GNP vs year, extending the data through 1995. What GNP does your trendline predict for 1993? Explain in the context of the problem.
5. In what year does the trendline predict the GNP will reach 6.6 trillion? Explain in the context of the problem.
FARM POPULATION
Consider the percent of the United States population which lived on farms during the years 1880-1990.
Year Percent 1880 43.8 1890 42.3 1900 41.9 1910 34.9 1920 3.1 1930 24.9 1940 23.2 1950 15.3 1960 8.7 1970 4.8 1980 2.7 1990 1.9
1. Using technology, calculate the average rate of change per year. You may, for example, make a table in a spreadsheet with Year, Percent of Population, and Average Rate of Change, as three columns. What are the independent and independent variables?
2. Using technology, create a plot of Percentage vs Year. Does the data appear to be linear? Explain.
3. Using technology, construct a linear trendline and determine the R2 value. What is the trendline equation? What is the slope, including units? What is the R2 value? Is there a strong or weak correlation?
4. Using the trendline formula, calculate algebraically the date when 100% of the population lived on a farm? Explain in the context of the problem.
5. Using the trendline formula, calculate algebraically the percent of the population you expect to be living on farms in the year 2000? Is this realistic? Explain in the context of the problem.
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