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MHT CET202019 Oct 2020Evening ShiftMathematicsDifferential EquationsActual

If the population grows at the rate of 8 % per year, then the time taken for the population to be doubled, is (Given 2=0 6912 )

Options

  1. A6 8 years
  2. B10 27 years
  3. C8 64 years
  4. D4 3 years

Correct answer

C. 8 64 years

Step-by-step solution

(D) P ₀ be the initial population and let the population after t years be 2 P ₀ . then, aligned dP dt &= 8 P 100 dP dt = 2 P 25 dP P &= 2 25 dt 1 P dP = 2 25 dt aligned P= 2 25 t+C ...(1) At, t=0, P=P₀ P₀= 2 0 25 +C C= P₀ P= 2 25 t+ P₀ P P₀ = 2 25 t t= 25 2 ( P P₀ ) When P=2 P₀t= 25 2 ( 2 P₀ P₀ )= 25 2 2=8.64

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