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
- A20( 2) years
- B10( 2) years
- C5( 2) years
- 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