If Pn = Population at the end of n decade, Po = Present population, Pav = Average arithmetic increase in the population (decadal), PI = Average incremental increase in population, n = Number of decades; what is the mathematical representation of Incremental Increase Method ?
- APn = PI × n + (Pav + Po)
- BPn = PI + (Pav + Po) × n
- CPn = Po + (Pav + PI) × nCorrect
- DPn = Po × n + (Pav + PI)
Solution
Concept
Incremental increase method of population forecast
Formula
Pn = P₀ + n Pav + n(n + 1)/2 · PI
Step-by-step solution
1. The incremental increase method adds the average arithmetic increase and the average incremental increase to the present population. 2. In its simplified form: Pn = P₀ + n (Pav + PI). 3. Only option (c) has this structure.
Explanation
The arithmetic increase n·Pav is corrected by the incremental term, which grows with the number of decades.
Why the other options are wrong
The other options multiply P₀ by n or add PI without the factor n, which does not represent a forecast from the present population.
Shortcut
Incremental increase: P₀ + n Pav + n(n+1)/2 PI.
Common mistake
Multiplying the present population by n.
Correct answer: C) Pn = Po + (Pav + PI) × n