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MHT CET202124 Sep 2021Evening ShiftMathematicsDifferential EquationsActual

A population P grew at the rate given by the equation dp dt =0.05 P , then the population will become double in

Options

  1. A20( 2) years
  2. B10( 2) years
  3. C5( 2) years
  4. D12( 2) years

Correct answer

A. 20( 2) years

Step-by-step solution

aligned & d p d t =0.05 P & d p 0.05 p = d t 20 d p P = d t & 20 |P|=t+c & When t=0, P=P c=20 |P| & 20 |P|=t+20 |P| aligned When t =0, P = P c =20 | P | 20 | P |= t +20 | P | When population doubles, we write aligned & 20 |2 P |= t +20 | P | & t =20 |2 P |-20 | P |=20[ |2 P |- | P |] & =20 [ | 2 P P | ] & =20( 2 ) years aligned

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