Percentage Population Related Mathematical Problems

Percentage Population Related Mathematical Problems

If the original population of a locality (i.e. region) be P and the annual growth rate be r%. The Population after n years

= P(1 + r/100)^n

change ( or increase) in the population

= P((1 +r/100)^n - 1)

if there is decrease in population be r% then

total population after n years = P ( 1 - r/ 100)^n

and decrease in population = P ( 1- (1- r/100)^n )

Example 1

If the annual increase in the population be 20% and the present population be 10,000. What will be the population after 3 years hence?

Solution:

10,000 (1+ 20/100)^3  = 10,000 (6/5)^3

= 10,000 x (1.2)^3 = 17,280

Example 2:

The Population of a town in the first year increase by 10% in the next year it decrease by 10% once again in the third year it increase by 10% and in the fourth year it decrease by 10%. If the present population be 20,000 then the population after four year will be:

Solution:

20,000 (1+ 10/100) (1- 10/100) (1+ 10/100) ( 1- 10/100)

= 20,000 (1.1) (0.9) (1.1) (0.9) 

= 20,000 x 121 x 0.81 x 

= 19,602