Logistic Growth Differential Equation Example (Deer Population Model) скачать в хорошем качестве

Logistic Growth Differential Equation Example (Deer Population Model)

In this example problem, we model a deer population using the logistic growth equation. A state park introduces 100 deer into a protected habitat. The carrying capacity of the park is 1000 deer, and the intrinsic growth rate is 0.6 per year. We: • Set up the logistic differential equation • Separate variables • Use partial fractions • Solve for the population function P(t) • Apply the initial condition • Analyze the long-term behavior Logistic model: dP/dt = rP(1 − P/K) P(0) = 100 r = 0.6 K = 1000 Final population model: P(t) = 1000 / (1 + 9e^(−0.6t)) We also examine: lim (t → ∞) P(t) = 1000 This example clearly shows how population growth slows as it approaches carrying capacity. This video is part of my Differential Equations examples series. Differential Equations playlists:    / @understandthemath   Guided notes and additional resources: https://www.understandthemath.com ODE Videos    • Ordinary Differential Equations Full Cours...      • How to Classify a Differential Equation (O...      • Slope Fields Explained Visually (Step-by-S...      • How to Analyze Autonomous Differential Equ...      • How to Solve Separable Differential Equati...      • Solving First-Order Linear ODEs with an In...      • How to Solve Exact Differential Equations      • How to Solve Homogeneous Differential Equa...      • How to Solve Bernoulli Differential Equations      • Modeling with First-Order Differential Equ...      • Euler’s Method Explained (Numerical Approx...      • Differential Equations Midterm Review | Fi...   Connect & Support TikTok:   / understandthemath   Instagram:   / understandthemath   Facebook: https://www.facebook.com/profile.php?... Support: https://buymeacoffee.com/understandth... More About Understand The Math Understand The Math offers clear, accessible, and engaging mathematics instruction for students and lifelong learners. I'm Cheryl Hile, the founder of Understand The Math, with a Ph.D. in Engineering Science and Applied Mathematics and over 25 years of university teaching experience. My goal is to provide accurate, high-quality math instruction through step-by-step explanations and carefully worked-out examples. Each video includes free guided notes, linked in the description. These notes help students follow along, highlight key concepts, and practice problems, making review easier and more effective. #DifferentialEquations #LogisticGrowth #PopulationModel #CarryingCapacity #FirstOrderODE #SeparableEquation #MathExamples #AppliedMath #CollegeMath #UnderstandTheMath