targas-edu.de
DE ☾ A+

Exponential growth

This page was translated from German with AI. It has not been checked by a native speaker. Original page in German

Always times the same number: \( y = a \cdot q^n \). From the chessboard with grains of wheat to compound interest.
📄 Open worksheet (PDF, German)

The video

Watch the colours: linear growth is blue, exponential growth is orange.

Subtitles are available in ten languages. Choose them at the bottom right of the video.

Contents of the video

  1. 0:00 Introduction
  2. 0:19 Always double
  3. 0:45 Linear or exponential?
  4. 1:13 The formula
  5. 1:36 Compound interest
  6. 2:00 Exponential decay
  7. 2:19 Try it yourself

The most important points

A legend: one grain of wheat on the first square of the chessboard, on every next square twice as many. Square \( n \): \( 2^{n-1} \) grains. Square 64: \( 2^{63} \approx 9.2 \cdot 10^{18} \).

Linear ( +2 ) against exponential ( · 2 ): from day 3 on, B is bigger.
Linear (\( +2 \)) against exponential (\( \cdot 2 \)): from day 3 on, B is bigger.

Exponential growth

\( y = a \cdot q^n \): start value \( a \), growth factor \( q \), number of steps \( n \). \( q > 1 \): growth, \( 0 < q < 1 \): decay.

Chessboard: every square twice as many grains.
Chessboard: every square twice as many grains.

Compound interest: \( 5\;\% \rightarrow q = 1.05 \). \( 1000 \cdot 1.05^{10} \approx 1628.89 \) €. Decay: \( q = 0.5 \): \( 100 \rightarrow 50 \rightarrow 25 \rightarrow 12.5 \).

Exponential decay with the factor 0.5 .
Exponential decay with the factor \( 0.5 \).

The worksheet

Here you can see the worksheet for the video (in German). First it explains everything again, then there are practice tasks at three levels. You can also open it as a PDF and print it.

📄 Open worksheet (PDF, German)

The worksheet – Page 1
Page 1/5
The worksheet – Page 2
Page 2/5
The worksheet – Page 3
Page 3/5
The worksheet – Page 4
Page 4/5
Show the worksheet solutions
The worksheet – Page 5
Page 5/5

Try it yourself

Task

Calculate: a) \( 100 \cdot 2^5 \) b) \( 3\;\% \rightarrow q = \;? \) c) \( -10\;\% \rightarrow q = \;? \) d) \( 1000 \cdot 1{,}1^2 \)

Show solution

a) \( 3200 \) b) \( 1{,}03 \) c) \( 0{,}9 \) d) \( 1210 \)

Keep learning with a language model

You are my maths teacher. I am learning German as a second language. Our topic: exponential growth (y = a times q to the n, growth factor, percentages, compound interest, decay). Give me five short tasks, one after the other. Always wait for my answer. Then tell me if it is right and explain briefly why. Write in simple German and put an English translation in brackets after each sentence.

How this was made: The idea, structure and examples of the series are mine. I made them with the help of AI: a language model (LLM) built the slides of the video following my instructions. The voice was generated with Qwen3-TTS, modelled on my own voice.

The subtitles, the translations, the worksheet and this page were also made with the help of AI. The translations have not been checked by native speakers.

The videos, worksheets, texts and prompts in this series are licensed under CC BY 4.0: you may use, change and share them if you name the source.