Logistic growth Knowledge-Based Download PDF

Questions

1. 1.

   According to the logistic growth model, what occurs when a population's size (N) exceeds the environmental carrying capacity (K)?

   • A) The carrying capacity increases proportionally to support the excess individuals indefinitely.
   • B) The population growth rate becomes negative, causing the population size to decline toward K.
   • C) The intrinsic rate of increase permanently drops to zero, halting all future births.
   • D) The population size stabilizes at that elevated level without experiencing higher mortality.
2. 2.

   In a population growing according to the logistic growth model, which condition occurs when the population size reaches the carrying capacity ($K$) in a closed system?

   • A) The birth rate equals the death rate, resulting in zero net population growth.
   • B) The birth rate reaches its theoretical maximum while the death rate drops to zero.
   • C) Environmental resistance ceases to exert limiting pressure on population numbers.
   • D) The per capita population growth rate reaches its highest positive value.
3. 3.

   In the logistic growth model, what happens to the per capita population growth rate as population size ($N$) approaches the carrying capacity ($K$)?

   • A) It remains constant at the intrinsic rate of increase regardless of density.
   • B) It gradually declines and approaches zero.
   • C) It increases exponentially due to greater reproductive contact.
   • D) It becomes negative immediately once the population surpasses half of the carrying capacity.
4. 4.

   In the logistic growth equation $\frac{dN}{dt} = rN\left(\frac{K - N}{K}\right)$, what does the expression $\frac{K - N}{K}$ represent?

   • A) The intrinsic per capita rate of population increase under ideal conditions
   • B) The absolute number of individuals added to the population per unit time
   • C) The maximum population size that a specific habitat can sustainably support
   • D) The proportion of carrying capacity that remains unused and available for further growth
5. 5.

   In a biological population exhibiting logistic growth, at which point is the absolute population growth rate ($dN/dt$) at its maximum?

   • A) When the population size is very close to zero
   • B) When the population size reaches the carrying capacity
   • C) When the population size is approximately half of the carrying capacity
   • D) When the per capita growth rate reaches zero