Problems on Population Growth

Concept Explanation

Problems on Population Growth

In our day to day life we observe that there are things or entities like population of city, the value of property, the height of a tree, weight and height of a child, the number of bacteria etc. which increase in magnitude over a period of time.

Growth: The relative increase in a quantity or entity is called growth .

Rate of Growth: Growth per unit of time is called the rate of growth.

Formulae for population Growth:

Formula 1: Let P be the population of a city or a town at the beginning of a certain year and the population grows at a constant rate of R% per annum, then

Population after n years = $Pleft ( 1+frac{R}{100} right )^{n}$

Formula 2: Let P be the population of a city or a town at the beginning of a certain year. if the population grows at the rate of $R_{1}%$ during second year, then

Population after 2 years = $Pleft ( 1+frac{R_{1}}{100} right )times left ( 1+frac{R_{2}}{100} right )$

This formula may be extended for more than 2 years.

Formula 3: Let P be the population of a city or a town at the beginning of a certain year. If the population decreases at the rate of R% per annum, then

Population after n years = $Pleft ( 1-frac{R}{100} right )^{n}$

Illustration: The population of a village is 20000. If the annual birth rate is 4 % and the annual death rate 2%., calculate the population after two years.

Solution: We have,

Annual birth rate = 4%

Annual death rate = 2%

So, Annual growth = ( 4 - 2) = 2 %

Thus, we have

P = Initial population = 20000, Rate of growth = 2% per annum, n = 2 years

So, Population after 2 years = $Pleft ( 1+frac{R}{100} right )^{n}$

$=20000left ( 1+frac{2}{100} right )^{2}$

$=20000left ( 1+frac{1}{50} right )^{2}$

$=20000left ( frac{51}{50} right )^{2}$

$=20000times frac{51}{50}times frac{51}{50}$

$=20808$

Hence population of the town after 2 years = 20808.

Sample Questions

(More Questions for each concept available in Login)

Question : 1

A factory increased its production of three wheelers from 80000 in 1999 to 92610 in 2002. Find the annual rate of growth of production of three wheelers.
A. 15%	B. 25%	C. 10%	D. 5%
Right Option : D
View Explanation

Question : 2

1000 workers were employed to construct a river bridge in four years. At the end of first year, 10% workers were retrenched. At the end of second year, 5% of the workers at that time were retrenched . However to complete the project in time the number of workers was increased by 10% at the end of third year. How many workers were working during the fourth year?
A. 9520	B. 9450	C. 9405	D. 9045
Right Option : C
View Explanation

Question : 3

The population of a town 2 years ago was 62500. Due to migration of cities, it declares every year at the rate of 4% per annum. Find its present population.
A. 5760	B. 56700	C. 57600	D. 507600
Right Option : C
View Explanation

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