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.)