Question

Mitscherlich's equation is expressed by the equation:

• A. \(\log (A + Y) = \log A - Cb\)
• B. \(\log (A - Y) = \log A - Cb\)
• C. \(\log (A - Y) = \log A + Cb\)
• D. \(\log (A - Y) = \log A - Cb^2\)

Hint:

Mitscherlich equation: \(\log (A - Y) = \log A - Cb\).
Law of diminishing returns.
Used in fertilizer response studies.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Mitscherlich's equation describes the relationship between crop yield and nutrient supply.
It is a law of diminishing returns.

Step 2: Key Formula or Approach:
Mitscherlich's equation: \(\frac{dY}{dx} = c(A - Y)\).
Integrating gives: \(\log (A - Y) = \log A - Cb\).

Step 3: Detailed Explanation:
A is the maximum possible yield.
Y is the yield obtained.
b is the amount of nutrient applied.
C is the proportionality constant.
The integrated form is \(\log (A - Y) = \log A - Cb\).
This indicates that yield increases with nutrient application but at a decreasing rate.

Step 4: Final Answer:
Mitscherlich's equation is \(\log (A - Y) = \log A - Cb\).
Hence, the correct option is (B).