Home/Calculus II/Elementary differential equations/Logistic modelSection 16.3Logistic modelFormulavizCopy LaTeXdPdt=kP(1−PK),\frac{dP}{dt}=kP\left(1-\frac{P}{K}\right),dtdP=kP(1−KP),View detail →where KKK is the carrying capacity. For P(0)=P0>0P(0)=P_0>0P(0)=P0>0:FormulaCopy LaTeXP(t)=K1+(K−P0P0)e−kt.P(t)=\frac{K}{1+\left(\frac{K-P_0}{P_0}\right)e^{-kt}}.P(t)=1+(P0K−P0)e−ktK.View detail →
FormulavizCopy LaTeXdPdt=kP(1−PK),\frac{dP}{dt}=kP\left(1-\frac{P}{K}\right),dtdP=kP(1−KP),View detail →
FormulaCopy LaTeXP(t)=K1+(K−P0P0)e−kt.P(t)=\frac{K}{1+\left(\frac{K-P_0}{P_0}\right)e^{-kt}}.P(t)=1+(P0K−P0)e−ktK.View detail →