Let the initial population be P_o.

And the population after time t be P.

According to question,

⇒

⇒

⇒

Integrating both sides, we have

⇒ 20∫ = ∫dt

⇒ 20log|P| = t + c ……(1)

Given, we have P = P_o when t = 0 sec

Putting the value in equation (1)

∴ 20log|P| = t + c

⇒ 20log|P_o| = 0 + c

⇒ c = 20log|P_o| ……(2)

Putting the value of c in equation (1) we have,

20log|P| = t + 20log|P_o|

⇒ 20log|P| – 20log|P_o| = t

⇒ 20(log |P| – log|P_o|) = t

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⇒ 20log ( = t ……(3)

Now, for the population to be doubled

Let P = 2P_o at time t1

∴ t = 20log (

⇒ t1 = 20log (

⇒ t1 = 20 log2

∴ time required for the population to be doubled = 20 log2 years