For rmax = 2.0, which sequence correctly lists the growth rates for the four Ns above carrying capacity?

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Multiple Choice

For rmax = 2.0, which sequence correctly lists the growth rates for the four Ns above carrying capacity?

Explanation:
When a population sits above carrying capacity, its growth rate becomes negative because the environment can’t support more individuals, so the net change in population declines. In the logistic framework, the growth rate is described by dN/dt = r max × N × (1 − N/K). With r max equal to 2.0, the term (1 − N/K) is negative for N > K, and the farther N is above K, the larger the magnitude of the negative rate. So the growth rates for the Ns above carrying capacity should be negative and become more negative as N increases beyond K. The sequence that shows increasingly large negative values aligns with this pattern, which is why the option with values like -20, -213, -583, -1333 fits best—the population is being driven downward more strongly as it sits further above capacity. The other sequences don’t display this consistent, steepening negativity as N rises above K, so they don’t match the logic of the logistic decline above carrying capacity.

When a population sits above carrying capacity, its growth rate becomes negative because the environment can’t support more individuals, so the net change in population declines. In the logistic framework, the growth rate is described by dN/dt = r max × N × (1 − N/K). With r max equal to 2.0, the term (1 − N/K) is negative for N > K, and the farther N is above K, the larger the magnitude of the negative rate. So the growth rates for the Ns above carrying capacity should be negative and become more negative as N increases beyond K. The sequence that shows increasingly large negative values aligns with this pattern, which is why the option with values like -20, -213, -583, -1333 fits best—the population is being driven downward more strongly as it sits further above capacity. The other sequences don’t display this consistent, steepening negativity as N rises above K, so they don’t match the logic of the logistic decline above carrying capacity.

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