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.
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 =
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 during second year, then
Population after 2 years =
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 =
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 =
Hence population of the town after 2 years = 20808.
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. | |||
Right Option : D | |||
View Explanation |
In a factory the production of scooters rose to 48400 from 40000 in 2 years. Find the rate of growth per annum. | |||
Right Option : A | |||
View Explanation |
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. | |||
Right Option : D | |||
View Explanation |
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