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(A) We analyze the population growth rate and migration rate starting from the year $2011$.The growth rate follows an $A.P.$ with first term $a = 5$ a

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$2016$

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(A) We analyze the population growth rate and migration rate starting from the year $2011$.The growth rate follows an $A.P.$ with first term $a = 5$ and common difference $d = 5$. The rate for year $n$ is $R_g(n) = 5n$.The migration rate follows a $G.P.$ with first term $a = 1$ and common ratio $r = 2$. The rate for year $n$ is $R_m(n) = 1 \cdot 2^{n-1}$.We compare these rates year by year:YearGrowth Rate $(A.P.)$Migration Rate $(G.P.)$$2011$ $(n=1)$$5 \%$$1 \%$$2012$ $(n=2)$$10 \%$$2 \%$$2013$ $(n=3)$$15 \%$$4 \%$$2014$ $(n=4)$$20 \%$$8 \%$$2015$ $(n=5)$$25 \%$$16 \%$$2016$ $(n=6)$$30 \%$$32 \%$In the year $2016$,the migration rate $(32 \%)$ exceeds the population growth rate $(30 \%)$. Therefore,the first fall in population will be witnessed in the year $2016$.

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