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The growth rate of a population in an un...

The growth rate of a population in an unlimited environment

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

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The correct Answer is:
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.
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