Time to double the amount of cultivated land
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Suppose we express the amount of land under cultivation as the product of four factors:
Land = (land/food) x (food/kcal) x (kcal/person) x (population)
The annual growth rates for each factor are:
1) the land required to grow a unit of food, -1% (due to greater productivity per unit of land)
2) the amount of food grown per calorie of food eaten by a human, +0.5%
3) per capita calorie consumption, +0.1%
4) the size of the population, +1.5%.
At these rates, how long would it take to double the amount of cultivated land needed? At that time, how much less land would be required to grow a unit of food?
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Solution Summary
With the application of logarithmic function and exponential function, the solution is comprised of detailed calculation of time needed to double the cultivated land, which is affected by four different growth factors.
Solution Preview
Since the annual growth rate for the land required growing a unit of food is -1%, at the nth year, the land required to grow a unit of food is (1-1%)^n.
Similarly, at the nth year, the amount of food grown per calorie of food eaten by a human is ...
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