Concept explainers
To find: The data in the table below represent the number of dairy farms (in thousands) and the amount of milk produced (in billions of pounds) in the United States for various years.
Year | Dairy Farms (thousands) | Milk produced (billion pounds) |
1980 | 334 | 128 |
1985 | 269 | 143 |
1990 | 193 | 148 |
1995 | 140 | 155 |
2000 | 105 | 167 |
2005 | 78 | 177 |
2010 | 63 | 193 |
a. Using a graphing utility, draw a
To find: The data in the table below represent the number of dairy farms (in thousands) and the amount of milk produced (in billions of pounds) in the United States for various years.
Year | Dairy Farms (thousands) | Milk produced (billion pounds) |
1980 | 334 | 128 |
1985 | 269 | 143 |
1990 | 193 | 148 |
1995 | 140 | 155 |
2000 | 105 | 167 |
2005 | 78 | 177 |
2010 | 63 | 193 |
b. Using a graphing utility, build a logarithmic model from the data.
To find: The data in the table below represent the number of dairy farms (in thousands) and the amount of milk produced (in billions of pounds) in the United States for various years.
Year | Dairy Farms (thousands) | Milk produced (billion pounds) |
1980 | 334 | 128 |
1985 | 269 | 143 |
1990 | 193 | 148 |
1995 | 140 | 155 |
2000 | 105 | 167 |
2005 | 78 | 177 |
2010 | 63 | 193 |
c. Graph the logarithmic function found in part (b) on the scatter diagram.
To find: The data in the table below represent the number of dairy farms (in thousands) and the amount of milk produced (in billions of pounds) in the United States for various years.
Year | Dairy Farms (thousands) | Milk produced (billion pounds) |
1980 | 334 | 128 |
1985 | 269 | 143 |
1990 | 193 | 148 |
1995 | 140 | 155 |
2000 | 105 | 167 |
2005 | 78 | 177 |
2010 | 63 | 193 |
d. In 2008, there were 67 thousand dairy farms in the United States. Use the function in part (b) to predict the amount of milk produced in 2008.
To find: The data in the table below represent the number of dairy farms (in thousands) and the amount of milk produced (in billions of pounds) in the United States for various years.
Year | Dairy Farms (thousands) | Milk produced (billion pounds) |
1980 | 334 | 128 |
1985 | 269 | 143 |
1990 | 193 | 148 |
1995 | 140 | 155 |
2000 | 105 | 167 |
2005 | 78 | 177 |
2010 | 63 | 193 |
e. The actual amount of milk produced in 2008 was 190 billion pounds. How does your prediction in part (d) compare to this?
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College Algebra Enhanced with Graphing Utilities Plus MyLab Math with Pearson eText -- Access Card Package (7th Edition) (Sullivan & Sullivan Precalculus Titles)
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