The e-function and exponential growth processes

The e-function and exponential growth processes is a ready-to-use Math teaching resource for Grades 10–12. This series introduces Euler's number e and the natural exponential function e^x step by step. Starting from a vivid approach via continuous compound interest, the properties of the e-function, its special derivative (e^x)' = e^x and the chain rule are developed.

Guiding question: How do we describe and calculate exponential growth and decay with the e-function?

What's included

• 5 differentiated worksheets with required and optional tasks
• Full answer keys with expected solutions
• A 7-slide colour presentation
• A detailed, step-by-step lesson plan
• Print & digital — editable and ready to use, no prep required

Learning objectives

• Describe Euler's number e and the natural exponential function e^x with its properties.
• Apply the laws of powers to e-functions and use the special derivative (e^x)' = e^x and the chain rule.
• Set up exponential models N(t) = N0 · e^(k·t) for real situations and determine the parameters from data.
• Compute half-life and doubling time and investigate exponential processes quantitatively.
• Interpret results in context and evaluate the scope and limits of exponential models.

Topics covered (5 worksheets)

• Getting to know e and the natural exponential function
• Calculating and differentiating with e-functions
• Setting up growth and decay models
• Analysing and interpreting models
• Word problems: half-life, doubling time and applications

How to use it

Teach the full series in sequence or pull single worksheets as stand-alone lessons. Differentiation is built in through required and optional tasks, so you can meet a range of levels in the same class. The included lesson plan and complete answer keys make the resource ready to teach with no additional preparation.

Frequently asked questions

What grade level is The e-function and exponential growth processes for?
It is designed for Grades 10–12 (Math), and the differentiated tasks let you adapt it up or down a level.

What file formats are included?
You receive editable Microsoft Word worksheets and answer keys, an editable PowerPoint presentation, and a Word lesson plan — all print-ready and suitable for digital classrooms.

Is it ready to use without preparation?
Yes. Everything is classroom-ready: print the worksheets or share them digitally, present the slides, and use the answer keys and lesson plan as-is.

Created with support from ChatGPT (OpenAI) and Claude (Anthropic).