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

The population of a town was 160000 three years ago. If it has been increased by 3%, 2.5% and 5% in the last three years, find the present population of the town.
A. 177366	B. 17736	C. 17366	D. 173766
Right Option : A
View Explanation

Question : 2

24000 blood donors were registered with a charitable hospital. The number of donors increased at the rate of 5% every six months. Find the time period at the end of which the total number of blood donors becomes 27783.
A. $frac{3}{2}$	B. $frac{1}{2}$	C. $frac{5}{2}$	D. none of these
Right Option : A
View Explanation

Question : 3

The present population of a city is 9261000. If it has been increasing at the rate of 5% per annum, find its population 3 years ago.
A. 80000	B. 800	C. 800000	D. 8000000
Right Option : D
View Explanation

Chapters

Problems On Boats And Stream

Rules For Divisibility

Square and Square Root

Profit Loss and Discount

Simple and Compound Interest

Ratio and Proportion

Partnership and Mixture

Time, Speed and Distance

Quadratic Equations

Time and Work

Mensuration

Surface Area and Volume

Introduction to Trigonometry

Permutation and Combination

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Computer Proficiency

Navodaya Entrance 6th & 9th

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