notes

Growth

sd exponential growth

Example: Population growth with feedback. Stock: Population $P$ Flow: Birth rate proportional to population, where $r$ is the growth rate, then more people lead to more births, reinforcing growth. Behavior: Exponential growth. Equation: $$\tag{SD2} \frac{dP}{dt} = rP. $$ Diagram: graph LR; Population -->|Influences| BirthRate BirthRate -->|Increases| Population

sd linear growth

Example: Population growth without feedback. Stock: Population $P$ Flow: Birth rate $b$ (constant). Behavior: Population increases at a steady rate. Equation: $$\tag{SD1} \frac{dP}{dt} = b. $$ Diagram: graph TD; Population -->|+ Constant Birth Rate| Population