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Lesson Packs · Grade 12 · Mathematics

Separable Differential Equations and Exponential Growth

Students learn what a differential equation and its solutions are, solve separable equations by separating the variables and integrating, use initial conditions to find particular solutions, and model exponential growth, decay, half-life and cooling.

Unit 5 · Lesson 18 · Differential Equations

Preview

Separable Differential Equations and Exponential Growth — Slide 1
  • Separable Differential Equations and Exponential Growth — Slide 4
    Slide 4
  • Separable Differential Equations and Exponential Growth — Slide 7
    Slide 7
  • Separable Differential Equations and Exponential Growth — Slide 16
    Slide 16
  • Separable Differential Equations and Exponential Growth — Slide 17
    Slide 17
  • Separable Differential Equations and Exponential Growth — Worksheet, page 1
    Worksheet, page 1
  • Separable Differential Equations and Exponential Growth — Answer key, page 1
    Answer key, page 1

Learning objectives

  • Verify by substitution that a function is a solution of a differential equation.
  • Solve separable differential equations and use an initial condition to find a particular solution.
  • Model growth and decay with dy/dt = ky, and use y = y₀eᵏᵗ to solve problems on half-life and cooling.

What's inside

  • 37 PowerPoint slides: lesson, worked examples and the worksheet with solutions
  • 10 worksheet questions (32 marks) with step-by-step solutions
  • Printable worksheet (3 pages) and a teacher answer key
  • Fully editable in PowerPoint, Google Slides, Keynote and Word

Questions teachers ask

Can I edit the files?

Yes. The PowerPoint and the Word worksheet are fully editable, so you can change examples, add questions or adapt the design for your class.

How do I use the worksheet slides?

After the teaching slides, each worksheet question appears on its own slide. Let students try it first, then show the next slide and work through the solution together.

Is there an answer key?

Yes. The Word file ends with a teacher answer key that has the answer and a worked solution for every question. It is also included as a separate PDF.

Which languages are available?

Every Lesson Pack is made in 18 languages: English, Simplified Chinese, Hindi, Spanish, Arabic, French, Bengali, Portuguese, Indonesian, Urdu, Vietnamese, Albanian, Italian, German, Turkish, Malay, Greek and Traditional Chinese (Hong Kong).

Do downloads count toward my plan?

Yes. Sign in with your free KiwiBee account to download. Each download counts toward your plan's daily and monthly download limit, the same as worksheets.