The growth rate of a population in an unlimited environment

Options

A. is described by an S-shaped curve
B. is greater than the intrinsic rate of increase
C. ls equal to (b - d)N
D. Depends on competition for resources

Answer

To understand the growth rate of a population in an unlimited environment, we can break down the concept into several steps:

### Step-by-Step Solution:

1. **Definition of Population Growth**:
- Population growth refers to the increase in the number of individuals in a population over time.

2. **Unlimited Environment**:
- An unlimited environment is characterized by an abundance of resources such as food, space, and other necessities that allow populations to grow without constraints.

3. **Exponential Growth**:
- In an unlimited environment, populations tend to exhibit exponential growth. This means that the population size increases at a constant rate over time, leading to a J-shaped curve when graphed.

4. **Mathematical Representation**:
- The growth rate of a population can be mathematically expressed using the equation:
\[ \frac{dn}{dt} = (b - d) \cdot n \]
- Here, \( \frac{dn}{dt} \) represents the change in population size over time, \( n \) is the current population size, \( b \) is the birth rate, and \( d \) is the death rate.

5. **Intrinsic Rate of Natural Increase**:
- The term \( (b - d) \) is known as the intrinsic rate of natural increase. It indicates the potential growth rate of the population when resources are not limited.

6. **Conclusion**:
- Therefore, the growth rate of a population in an unlimited environment is represented by the equation \( \frac{dn}{dt} = (b - d) \cdot n \), confirming that the population grows exponentially.

### Final Answer:
The growth rate of a population in an unlimited environment is given by the equation:
\[ \frac{dn}{dt} = (b - d) \cdot n \]
where \( b \) is the birth rate, \( d \) is the death rate, and \( n \) is the population size.