Question

If there is a policy that 1/3rd of population of a community has migrated every year from one place, to some other place, what is the leftover population of that community after the sixth year, if there is no further growth in the population during this period

Answer 1

Answer:

as the population decreases every ear by 1/3

therefore if you do 1/3 + 1/3 of 1/3 +1/3of 1/3 of 1/3 and so on 6 times

1/3+(1/3×1/3)+(1/3×1/3×1/3)+(1/3×1/3×1/3×1/3)+(1/3×1/3×1/3×1/3)+(1/3×1/3×1/3×1/3×1/3)

which will give the anwer = 1/3 raise to the power 15

that means that the 1/3 raise to the power 15 of the total population has left the community

=1/14348907

has left the community

left is 14348906/14358907

Answer 2

Explanation:

let the initial population was x

after the first year  it will be

$x-\frac{x}{3} \\\\x(1-\frac{1}{3}) \\\\=\frac{2x}{3}$

after the second year ,

population will be

$\frac{2x}{3}\times (1-\frac{1}{3}) \\\\\= (\frac{2}{3})^2 x$

similarly after the sixth year

population

$(\frac{2}{3})^6x \\\\= (\frac{64}{729} )x$

i.e

$\frac{64}{729} ^t^h$ part of the original population

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