Formulae For Population Decrease Or De-Growth –
1) Let there be an decrease in population at R% per annum
R
a) Then, population after n years = P X ( 1 - ------- )
100
P
b) Population n years ago = -----------------------
R
( 1 - --------- )ⁿ
100
Example.1) If in a town the population 2 years ago was 50000. Due to migration to cities, it decrease at 5% per annum. Find it’s present population.
Ans.) As per the given condition, population 2 years ago = 50000, n = 2, P = ?, R = 5%
As we know the formulae -
P
Population n years ago = ----------------------
R
( 1 - --------- )ⁿ
100
P
Or, 50000 = ------------------
5
( 1 - --------- )²
100
P
Or, 50000 = --------------------
1
( 1 - ------- )²
20
P
Or, 50000 = --------------------
19
( ------- )²
20
19 X 19
Or, P = 50000 X --------------
20 X 20
Or, P = 125 X 19 X 19 = 45125
So, the current population of the town is 45125 (Ans.)