Modeling Populations with Calculus

Calculus lets us model how populations grow or shrink over time. We use differential equations, limits, and series to understand real-world scenarios like bacteria growth, animal populations, or even viral spread.

• Exponential models: \( P(t) = P_0 e^{kt} \)
• Logistic growth: \( P(t) = \frac{L}{1 + e^{-k(t-t_0)}} \)

These models are used to predict trends, allocate resources, or plan conservation efforts.