Population density at time $t+1$ is typically expressed as:
$Nt+1=Nt+(\{B+I\}-\{D+E\})$, where $B+I$ is,
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Inversely proportional to D + E
We are given the population growth equation:
Nt+1 = Nt+ (B + I - D - E)
Where:
- Nt= population size at time t
- B= births
- I = immigration
- D = deaths
- E = emigration
Here, (B + I) represents the inputs to the population (factors that increase population size).
- More births and immigration → population increases
- These are directly proportional to the population growth
Similarly, (D + E) represents the losses (factors that decrease population size).
Other options:
- Inversely proportional to B + I → makes no sense (B + I can’t be inversely proportional to itself).
- Directly proportional to E → E (emigration) reduces population, not increases.
- Directly proportional to D → D (deaths) reduces population too.
The correct interpretation: B + I is directly proportional to the increase in population size, but none of the given options say this exactly.
However, if population increases with B + I, it opposes D + E.
Hence, the only reasonable relation is: It is inversely proportional to D + E — when deaths and emigration increase, the relative effect of B+I decreases, and vice versa.
Correct Answer: Inversely proportional to D + E