Population Growth & Decay | Application of First-Order Differential Equations

Learn how to apply first-order differential equations to solve population growth and decay problems in this easy-to-follow math video. 📈 Whether you’re a student preparing for exams or just exploring real-life applications of differential equations, this lesson walks you through the derivation, solution methods, and real-world problems involving exponential growth and decay.

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🌟 In This Video:
• What is population growth and decay?
• Deriving the exponential growth model: dn/dt = rn
• Using both separable and linear methods to solve differential equations
• Difference between growth and decay (sign of the exponent)
• Real-life examples with interest rates and savings accounts
• Exam-style questions and assignments to test your understanding

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🎯 Who is this for?
• Students studying Calculus or Differential Equations
• Engineering & Math undergraduates
• Anyone preparing for exams (WAEC, NECO, JAMB, GCE, etc.)
• Math lovers curious about real-world applications

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🔖 Chapters / Timestamps

00:00 – Introduction to First-Order Differential Equations
01:30 – What is Population Growth & Decay?
03:20 – Deriving Growth Equation: dn/dt = rn
06:15 – Solving using Separable Equations
08:30 – Solving using Linear Equation Method
10:40 – Difference Between Growth and Decay
12:00 – Example 1: $20,000 at 5% Interest
15:30 – How Long to Double the Money?
18:20 – Assignment: Mixed Interest Rates (4+3 years)
20:00 – Example 2: Finding Interest Rate for Doubling
23:10 – Wrap-up & Intro to Next Topic (Temperature Problems)
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Видео Population Growth & Decay | Application of First-Order Differential Equations канала Maths Atoka