Question

Which of the following statements is correct regarding the given production function?

a) The population will grow indefinitely without bound.
b) The population will approach the carrying capacity
K as
t approaches infinity.
c) The growth rate
r has no effect on the population size.
d) The constant
C determines the initial population size.

Answer 1

The population will approach the carrying capacity as time progresses, exemplified by the logistic growth model with an S-shaped curve. The constant C sets the initial size, and growth rate r influences the rate of increase until reaching carrying capacity.

Step-by-step explanation:

The correct statement regarding the given production function and its impact on population dynamics is that the population will approach the carrying capacity K as time (t) approaches infinity. This is because initially, when resources are abundant, populations may grow exponentially. However, as the population size (N) increases and approaches the carrying capacity (K), resources become less available, and the growth rate slows down, eventually leveling off as the population reaches carrying capacity. This is well illustrated by the logistic growth model which produces an S-shaped curve. The constant C typically determines the initial population size, while the growth rate r positively influences the population increase until it is curtailed by reaching the carrying capacity, which acts as an upper limit on population size in a given environment.