MHT CET202123 Sep 2021Morning ShiftMathematicsVector AlgebraActual

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

A6.8 year
B4.3 years
C10.27 years
D8.64 years

Correct answer

D. 8.64 years

Step-by-step solution

Let the initial population be P and rate of increase is 8 % per year. aligned & dP dt = 8 100 P & dP P = 0.08 t & | P |=0.08 t + c aligned When t =0 , we get c = P P =0.08 t + P When ' P ' doubles, we write aligned & 2 p=0.08 t + P & ( 2 P P )= 2=0.6921=0.08 t & t = 0.6912 0.08 =8.64 years aligned

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