Let P0 be the initial population and let the population after t years be P. Then, ‌‌
dP
dt
=kP,‌ where ‌k>0 ‌⇒‌
dP
P
=k‌dt Integrating on both sides, we get ‌log‌P=kt+c ‌‌ When ‌t=0,P=P0 ∴‌‌log‌P0=0+c ∴‌‌c=log‌P0 ‌log‌P=kt+log‌P0 ‌⇒log‌
P
P0
=kt‌‌....(i) When t=6‌ hrs, ‌P=2P0 ∴‌‌log‌