Question

The equation below represents an alternate way to express the logistic growth equation, but it is equivalent to the equation from your text. What will occur in the population as the ratio N/K is increased? ΔN/Δt = rN (1 – N/K)

Answer 1

population growth rate slows

Explanation:

When N/K increases, the difference 1 - N/K gets smaller and so does the product rN(1 -N/K). That means ΔN/Δt get smaller.

ΔN/Δt is the rate of change of population, so ...

the rate of change of population will decrease as N/K increases.

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That's the point of the logistic equation. Population growth rate is proportional both to population and to the difference from the carrying capacity of the environment. As the population approaches the carrying capacity (N/K → 1), the difference gets smaller, so the population growth gets smaller.