Mitscherlich’s equation: An important agricultural problem is to determine how a quantity of nutrient, such as nitrogen, affects the growth of plants. We consider the situation wherein sufficient...

Mitscherlich’s equation: An important agricultural problem is to determine how a quantity of nutrient, such as nitrogen, affects the growth of plants. We consider the situation wherein sufficient quantities of all but one nutrient are present. One baule8 of a nutrient is the amount needed to produce 50% of maximum possible yield. In 1909 E. A. Mitscherlich proposed the following relation, which is known as Mitscherlich’s equation:9

Here b is the number of baules of nutrient applied, and Y is the percentage (as a decimal) of maximum yield produced.

a. Verify that the formula predicts that 50% of maximum yield will be produced if 1 baule of nutrient is applied.

b. Use functional notation to express the percentage of maximum yield produced by 3 baules of nutrient, and calculate that value. c. The exact value of a baule depends on the nutrient in question. For nitrogen, 1 baule is 223 pounds per acre. What percentage of maximum yield will be produced if 500 pounds of nitrogen per acre is present?