Question

? What will be the
population of a city for the
year 2031 by Geometric
increase method from the
following data Year
Population 1971 18000 1981
22400 1991 27200 2001
31600 2011 36700​

Answer 1

507804 is the population for the year 2031

Answer 2

Answer:

The population in the year 2031 is 45463

Step-by-step explanation:

The given population in certain years is mentioned as given below.

Population in year 1971 is

$p _{1971} = 18000$

Similarly the population in the years 1981,1991,2001&2011 are mentioned as follows

$p _{1981} = 22400 \\ p _{1991} =27200 \\ p _{2001} =31600 \\ p _{2011} = 36700$

The increament between 1971 and 1981 is

$= 22400 - 18000 = 4400$

Geometric rate of growth is calculated as

$\frac{4400}{18000} = 0.244$

Similarly the increament and geometric rate of growth between 1981 and 1991 is

$= 27200 - 22400 = 4800 \\ = \frac{4800}{22400 } = 0.214$

Thee increament and geometric rate of growth between 1991 and 2001 is

$= 31600 - 27200 = 4400 \\ = \frac{4400}{27200} = 0.161$

the increament and geometric rate of growth between 2001 and 2011 is

$= 36700 - 31600 = 5100 \\ = > \frac{5100}{31600} = 0.161$

Now the geometric mean of these rate of growths is calculated as follows

$I_{G} \\ = (0.244 \times 0.214 \times 0.161 \times 0.161) {}^{ \frac{1}{3} } \\ = 0.113$

Hence the population in the year 2021 is calculated as given below

$p _{2021} = 36700(1 + 0.113) \\ = 40847$

And the population in the year 2031 is calculated as

$p _{2031} = 36700(1 + 0.113) {}^{2} \\ = 45463$

Therefore,the population in the year 2031 is found to be 45463

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