Grain Yield

Beginning in about 1950, the world saw an unprecedented increase in the productivity of land. Modern agricultural techniques produced drought-resistant and disease-resistant strains of grains, improving the yield of land which previously had been only marginally productive. The effect was a significant increase in yield, measured in tons of grain produced per hectare. The table below gives average grain yield worldwide for selected years. The units are kilograms per hectare.

Year 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995
Yield 1060 1170 1280 1400 1650 1760 2000 2310 2540 2500

  1. Use regression to obtain a linear function Y(t) which best fits these data. Let t = 0 in the year 2000 and round your numbers to three decimal places. The function Y(t) will give the approximate grain yield in kilograms per hectare in year 2000 + t. Use the function Y(t) to complete this Group Work; also, save this function, it will be needed later.
  2. Predict the yield per hectare in the year 2000.
  3. When will the yield reach 3000 kilograms per hectare?
  4. According to the function, how much will the yield increase in a five year period? How does that compare with the actual change over five year periods as shown in the original data?

Return to Earth Math Home Page