Question

Match column I with column II and find out the correct option.

Column I	Column II
A. (b - d)	1. N ${}_t$ + [(B + I) - (D + E)]
B. dN/dt	2. r
C. N ${}_{t+1}$	3. N${}_o$e${}^{rt}$
D. N ${}_t$	4. rN

• A. A - 1, B - 3, C - 4, D - 2
  
• B. A - 2, B - 4, C - 1, D - 3
  
• C. A - 4, B - 3, C - 2, D - 1
  
• D. A - 2, B - 1, C - 3, D - 4
  

Answer 1

The correct option is B A - 2, B - 4, C - 1, D - 3


Intrinsic rate of natural increase or Malthusian parameter (r) is a parameter used to assess the impact of biotic and abiotic factors on population growth. It can be expressed as:
$r=(b-d)$
where,
b is birth rate i.e the number of live births per capita
d is death rate i.e number of deaths per capita

Population density is the number of individuals of a species per unit area at a given time. If the initial population density at time t is $N_t$, then the population density at time (t+1) can be represented as:
$N_{t+1}=N_t+\left[\right(B+I)-(D+E\left)\right]$
where,
B is natality i.e the number of live births during a given time period
I is immigration i.e the number of individuals of the same species that enter a population during a given time period
D is mortality i.e the number of deaths during a given time period
E is emigration i.e the number of individuals of the same species that leave a population during a given time period

The exponential growth model is shown by a population when the resources in its habitat are unlimited. In such a population, having a population density N, the increase or decrease in N during a time period t can be expressed as:
dN/dt = rN
where,
r is the intrinsic rate of natural increase

This growth model is represented by a J-shaped curve where N is plotted against time t. This curve is represented in the integral form as:
$N_t=N_o{e}^{rt}$
where,
$N_t$ is the population density at time t
$N_o$ is the population density at time zero
$r$ is the intrinsic rate of natural increase
$e$ is the base of natural logarithms