From 9bd224b9caa92824b8da4af47504fd8c6250fcce Mon Sep 17 00:00:00 2001 From: choisunmi00 Date: Thu, 26 Dec 2024 18:28:55 +0900 Subject: [PATCH] Update 2024-12-21-System dynamics.md --- _posts/2024-12-21-System dynamics.md | 7 +++---- 1 file changed, 3 insertions(+), 4 deletions(-) diff --git a/_posts/2024-12-21-System dynamics.md b/_posts/2024-12-21-System dynamics.md index db5e6fa..2fae1e4 100644 --- a/_posts/2024-12-21-System dynamics.md +++ b/_posts/2024-12-21-System dynamics.md @@ -32,7 +32,7 @@ math: true $$\frac{dN}{dt} = kN \Rightarrow N(t) = N_0 e^{kt}$$ - 1 + 1 @@ -40,9 +40,8 @@ math: true - $$$$ $$\frac{dN}{dt}$$ $$= (B - D)N = (B_0 - D_0 N)N$$ - $$= B_0 \left( 1 - \frac{D_0 N}{B_0} \right) N = r \left( 1 - \frac{N}{C} \right) N$$ - $$\Rightarrow N(t) = \frac{C N_0}{N_0 + (C - N_0)e^{-rt}}$$ - 1 + $$= B_0 \left( 1 - \frac{D_0 N}{B_0} \right) N = r \left( 1 - \frac{N}{C} \right) N\ \Rightarrow N(t) = \frac{C N_0}{N_0 + (C - N_0)e^{-rt}}$$ + 1