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AP EAMCET202021 Sep 2020Evening ShiftMathematicsApplication of DerivativesActual

The population of a city grows at the annual rate of (3 % ). What percentage increase is expected in (5 yr ) ?

Options

  1. A(12.9 % )
  2. B(13.9 % )
  3. C(14.9 % )
  4. D(15.9 % )

Correct answer

D. (15.9 % )

Step-by-step solution

Let the population in begining is (P₀ ), then according to the question percentage increase in 5 yr expected is ( aligned P₀ (1+ 3 100 )^5-P₀ P₀ 100 & = [ ( 103 100 )^5-1 ] 100 & = [(1.03)^5-1 ] 100 & =[1.159-1] 100=15.9 % aligned ) Hence, option (d) is correct.

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