Question

The following data have been noted from the census department.
Year Population
1960 9,000
1970 16,000
1980 19,000
1990 32,500
Calculate the probable population in the year of 2020 and 2040.

Answer 1

Answer:

In 2020- 46,000

2040- 57,000

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Answer 2

Answer:

Population in 2020 = 123407

Population in 2040 = 300362

Step-by-step explanation:

For 1960

Population = 9000

For 1970

Population = 16000

Increase in Population = 16000- 9000 = 7000

Percentage increase in population = $\frac{7000}{9000}*100$ = 77.78%

For 1980

Population = 19000

Increase in Population = 19000- 16000 = 3000

Percentage increase in population = $\frac{3000}{16000}*100$ = 18.75%

For 1990

Population = 32500

Increase in Population = 32500 - 19000 = 13500

Percentage increase in population = $\frac{13500}{19000}*100$ = 71.05%

Average percentage increase in population per decade(g) = (77.78% + 18.75% + 71.05% ) /3 = 56.01%

Let population after n decade = Pn

So,

$P_{n} = P(1 + \frac{g}{100} ) ^n$

For 2020, ie after 3 decade (n = 3) from 1990  

Pn = $32500(1+ \frac{56.01}{100})^3$

Pn = 123407

Population in 2020 = 123407

For 2040, ie after 5 decade (n = 5) from 1990  

Pn = $32500(1+ \frac{56.01}{100})^5$

Pn = 300362

Population in 2040 = 300362

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