👉 In this context, we're exploring the application of calculus and linear algebra to solve a real-world problem involving population dynamics. Specifically, we use differential equations, a branch of calculus, to model how a population changes over time. The logistic growth model, a common differential equation in this field, takes the form \( \frac{dP}{dt} = rP\left(1 - \frac{P}{K}\right) \), where \( P \) is the population size, \( r \) is the growth rate, and \( K \) is the carrying capacity of the environment. To analyze this model, we often employ techniques from linear algebra, such as finding equilibrium points and stability analysis, to understand long-term behavior and predict population trends.
