Practical Applications
## 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.
Examples
- Predicting how fast a virus spreads in a community using exponential growth equations.
- Calculating the sustainable fish population in a lake with logistic models.