Question

Verhulst- Pearl logistic growth described by the equation $\frac { dN }{ dt } = rN\left[ \frac { K-N }{ K } \right]$, where ‘r’ and ‘K’ represent
(a) r- intrinsic rate of natural decrease, K- carrying capacity
(b) r- intrinsic rate of natural increase, K- carrying capacity
(c) r- extrinsic rate of natural increase, K- productive capacity
(d) r- extrinsic rate of natural decrease, K- carrying capacity

Answer 1

Hint: The logistic population growth model and the Verhulst-Pearl equation associated with the rate of reproduction are proportional to both the existing population and the number of available resources.

Complete answer:
Two types of population growth patterns may occur depending on the environmental conditions and they are logistic growth and exponential growth. The population increases overtime at the start as there are few individuals and many resources. But when the number of individuals grows large resources are used up and start decreasing, slowing the growth rate. Thus the logistic growth produces an S-shaped curve graph and takes place when a population's per capita growth rate decreases as population size approaches a maximum of the carrying capacity. It can be given by the equation:
 $\frac { dN }{ dt } = rN\left[ \frac { K-N }{ K } \right]$
Where, N = Population density at time t, and as this increases, the rate of growth $\frac { dN }{ dt }$ decreases. 
r = Intrinsic rate of natural increase and it depends on population density and how close it is to carrying capacity. It is the rate at which a population increases in size if no density-dependent forces are regulating the population.
K = Carrying capacity, is the maximum population size of a biological species that can be supported in that specific environment, given the food, habitat, water, and other resources available.
So, the correct answer is 'r - intrinsic rate of natural increase, K - carrying capacity'.

Note: Exponential growth produces a J-shaped curve graph and takes place when a population's per capita growth rate stays the same, regardless of population size it makes the population grow faster and faster as it gets larger. It can be given by the equation:
$\frac { dN }{ dt } =rN$