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
- 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.
- Predict the yield per hectare in the year 2000.
- When will the yield reach 3000 kilograms per hectare?
- 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?
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