which of the following option is true for verhulst Pearl logistic growth?
(A)population growth is decreased by the equation `dN/dt = rN[K/(K-N)]`.
(B) r' represents biotic potential.
(C) applicable to a population growing in habitat with limited resources.
(D)K represents carrying capacity

Options

A. Only (A)
B. only (B)
C. A, B and D
D. B, C and D

Answer

To determine which of the options is true for Verhulst-Pearl logistic growth, let's analyze each option step by step.

### Step 1: Understanding the Equation
The logistic growth model is represented by the equation:
\[ \frac{dN}{dt} = rN \left(\frac{K-N}{K}\right) \]
Where:
- \( \frac{dN}{dt} \) = rate of change of population size
- \( r \) = intrinsic rate of increase (also known as biotic potential)
- \( K \) = carrying capacity of the environment
- \( N \) = current population size

### Step 2: Analyzing Each Option
**Option A:** "Population growth is decreased by the equation \( \frac{dN}{dt} = rN\left(\frac{K-N}{K}\right) \)."
- This statement is misleading. The equation describes how population growth slows down as it approaches the carrying capacity \( K \). It does not imply that growth is decreased by the equation itself; rather, it shows a model of growth that accounts for resource limitations.

**Option B:** "r represents biotic potential."
- This statement is true. In the logistic growth equation, \( r \) indeed represents the intrinsic rate of increase or biotic potential of the population.

**Option C:** "Applicable to a population growing in habitat with limited resources."
- This statement is also true. The logistic growth model is specifically designed to describe populations that grow in environments where resources are limited, leading to a carrying capacity \( K \).

**Option D:** "K represents carrying capacity."
- This statement is true. In the logistic growth equation, \( K \) is defined as the carrying capacity, which is the maximum population size that the environment can sustain.

### Conclusion
Based on the analysis:
- **Option A** is false.
- **Option B** is true.
- **Option C** is true.
- **Option D** is true.

Thus, the true options for Verhulst-Pearl logistic growth are **B, C, and D**.