[Campbell Biology P.1245] The text presents two primary mathematical expressions for populati... | Practice Question

The text presents two primary mathematical expressions for population growth: ΔN/Δt = rΔtN and dN/dt = rN. What is the most significant conceptual difference between these two equations?

  • A: The first equation applies only to bacterial populations, while the second applies to all species.
  • B: The first describes growth over a discrete time interval, while the second describes instantaneous growth at a specific moment.
  • C: The variable 'rΔt' in the first equation represents the absolute growth rate, while 'r' in the second represents the relative growth rate.
  • D: The first equation ignores immigration and emigration, while the second includes them.

Explanation

The equation ΔN/Δt = rΔtN describes the change in population size over a specific, discrete time interval Δt . In contrast, dN/dt = rN uses differential calculus to represent the rate of change at each instant in time dt , implying an infinitesimally small time interval. The text explicitly states that as Δt becomes shorter, Δt and dt become increasingly close, signifying the shift from discrete to instantaneous measurement.