Which of the following equations best describes exponential population growth in a population of rabbits with unlimited resources?

• A. \(\frac{dN}{dt} = N - rK\)
• B. \(\frac{dN}{dt} = rN\)
• C. \(\frac{dN}{dt} = K - rN\)
• D. \(\frac{dN}{dt} = rN\left(1 - \frac{N}{K}\right)\)

Answer: (B)

Verified step by step guidance

1. Step 1: Understand the concept of exponential population growth. Exponential growth occurs when a population grows at a constant rate over time, assuming unlimited resources and no environmental constraints. The growth rate is proportional to the current population size.
2. Step 2: Analyze the given equations. Each equation represents a different model of population growth. For exponential growth, the rate of change in population size (dN/dt) is directly proportional to the population size (N) and the intrinsic growth rate (r).
3. Step 3: Identify the equation that matches the characteristics of exponential growth. The equation \(rac{dN}{dt} = rN\) represents exponential growth because it shows that the change in population size depends only on the intrinsic growth rate (r) and the current population size (N).
4. Step 4: Compare the other equations to understand why they do not represent exponential growth. For example, \(rac{dN}{dt} = rN(1 - rac{N}{K})\) represents logistic growth, which includes a carrying capacity (K) that limits growth as the population approaches K. Similarly, \(rac{dN}{dt} = N - rK\) and \(rac{dN}{dt} = K - rN\) do not align with the principles of exponential growth.
5. Step 5: Conclude that the correct equation for exponential population growth in a population of rabbits with unlimited resources is \(rac{dN}{dt} = rN\), as it accurately describes the proportional relationship between population size and growth rate under ideal conditions.