According to the 2001 census,the population growth rate of Lucknow is going to be an increasing AP with first year's rate as 5% and common difference as 5% but simultaneously the migration,rate is an increasing GP with first term as 1% and common ratio of 2.If the population on 31 december 2000 is 1 million,thn find in which year will Lucknow witness its first fall in population?

• population growth rate according to the problem
  year 1 = 5%
  year 2 = 10%
  year 3 = 15%
  year 4 = 20%
  year 5 = 25%
  year 6 = 30%
  
  population decrease due to migration
  year 1 = 1%
  year 2 = 2%
  year 3 = 4%
  year 4 = 8%
  year 5 = 16%
  year 6 = 32%
  
  Thus, the first fall would happen in year 2006
• 8 years agoHelpfull: Yes(10) No(0)
• In sixth year i.e.2006,migration rate(2^5=32%) is more than the population growth rate (30%).
  So there will be first population fall in 2006.
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• fall in 2006
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• acc to my answer the downlfall is occur if migrating people sum is more than increasing population.
  total people will be sum in ap and gp.
  5% of 1million=5000000. common difference is 5%of 1 million 5000000.
  so sn=n/2*(2a+(n-1)d).
  sn=n/2*(5000000+(n-1)*5000000);
  solving this 2500000n*n.
  migration rate is same.
  a=1% of million =1000000
  sn=a(1-rpower(n))/(1-r);
  gn=1000000(1-2power(n))/1-2=1000000*2power(n);
  so put n=1,2,3,4,5,6,7,
  and check for gn>sn...
  but only 8 it decrease gnis greater then sn and 2008 is answer
  
• 8 years agoHelpfull: Yes(0) No(1)