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MHT CET202014 Oct 2020Morning 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. A8.64 years
  2. B6.8 years
  3. C10.27 years
  4. D4 3 years

Correct answer

A. 8.64 years

Step-by-step solution

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

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