AP Calculus BC
Advanced Placement Calculus BC including series, parametric equations, and polar functions.
Practical Applications
Analyzing Population Growth
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.