d P ( t ) d t = P ( t ) {\displaystyle {\frac {dP\left(t\right)}{dt}}=P\left(t\right)}
(Eq.3.1)
∫ d P P = ∫ d t ⇒ ln | P | = t ⇒ P ( t ) = c e t {\displaystyle \int {\frac {dP}{P}}=\int dt\Rightarrow \ln \left|P\right|=t\Rightarrow P\left(t\right)=ce^{t}}
(Eq.3.2)
P ( 0 ) = P 0 ⇒ c e 0 = P 0 ⇒ c = P 0 {\displaystyle P\left(0\right)=P_{0}\Rightarrow ce^{0}=P_{0}\Rightarrow c=P_{0}}
(Eq.3.3)
P ( t ) = P 0 e t {\displaystyle P\left(t\right)=P_{0}e^{t}}
(Eq.3.4)
