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.
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. | |||
Right Option : C | |||
View Explanation |
The bacteria in a culture grows by 10% in the first hour, decreases by 10% in the second hour and increases by 10% in the third hour.If the original count of the bacteria in a sample is 10000, find the bacteria count at the end of three hours. | |||
Right Option : B | |||
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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