# CLASS-9FINDING POPULATION GROWTH

GROWTH & DEPRECIATION

Growth – Some entities such as population, weight, and height of a child, height of house, etc., increase in magnitude over a period of time. The relative increase is called growth. Growth per unit of time is called the rate of growth.

Formula For Population Growth

Let there be an increase in population at R% per annum

R

a) Then, population after n years = P X ( 1 + -------- )ⁿ

100

P

b) Population n years ago = -----------------

R

( 1 + ------- )ⁿ

100

Example.1) The present population of a town is 176400. It increases at the rate of 5% per annum. Find (a) it’s population after 2 years, (b) its population 2 years ago

Ans.) The present population (P) = 176400, and Rate of increase (R) = 5% per annum

As we know the formula -

R

Then, population after n years = P X ( 1 + ------- )ⁿ

100

5

So, the population after 2 years = 176400 X (1 + ------- )²

100

105        105

=  176400 X ------- X ------- = 194481 …………..(a)  (Ans.)

100        100

Now, as per the formulae we know that -

P

Population n years ago = --------------------

R

( 1 + --------- )ⁿ

100

176400

Now, population 2 years ago or before = ------------------

5

( 1 + ------- )²

100

20            20

= 176400 X -------- X ---------

21            21

=  400 X 20 X 20  = 160000 ………………(b)   (Ans.)

So, population of that town after 2 years would be 194481 and 2 years before was 160000    (Ans.)