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 Home Grain Supply Calculus Supply versus Demand Per Capita Grain Supply

Area Cultivated

From 1950 to 1981 the amount of land cultivated for grain increased, reaching an all time high in 1981 At that time, land previously used for food production was shifted over to development and the amount of land cultivated for grain and other agricultural uses began to decline. The table below gives the amount of land cultivated for grain for selected years, beginning in 1981. The units are billion hectares (one hectare is about 2.46 acres)

 Year 1981 1983 1985 1987 1989 1991 1993 1995 Billion Hectares 0.732 0.706 0.715 0.685 0.694 0.687 0.677 0.666

Source: Wolrd Watch

Questions
1. Use regression to find the linear function A(t) which best fits the data in the table. Let t = 0 in the year 2000 so that A(t) gives the area cultivated for grain, measured in billion hectares, in year 2000 + t. Round your numbers to three decimal places.
Use the function A(t) to complete the remaining questions. Also, save this function, it will be needed later.
2. Predict the area cultivated in the year 2000.
3. Estimate the number of years will it take for the area to decrease by 0.100 billion hectares?
4. How much will the area decrease in a two year period? How does that compare with the actual change each two years as shown in the data?