Reason with a Logistic Population Model

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Use growth rate = rN(1 - N/K), where N is population size, r is a positive rate constant, and K is carrying capacity. Compare N with K before calculating. This continuous model is a simplification, not an exact forecast.

Worked example

If r = 0.2, N = 50, and K = 100, the modeled growth rate is 0.2 x 50 x (1 - 0.5) = 5 individuals per time unit. Real populations also face changing conditions.

Model Assumptions

For the calculations, use r = 0.1 per year and K = 200. Treat K as fixed within this model. Growth rate is a rate at the stated population size, not a count that must be added unchanged every year.

1. What is the modeled growth rate when N = 100, in individuals per year? Answer

2. What is the modeled growth rate when N = 200, in individuals per year? Answer

3. With N above K and positive r, what sign does the modeled growth rate have? Positive Negative Always zero

4. Why might a real habitat's carrying capacity change? A population model guarantees fixed resources The symbol K cannot be changed Its available resources can change

5. Why should the calculated rate not be added unchanged for many years? The rate depends on N, which changes as the population changes Growth rates never use time units A model cannot contain multiplication