# Resources suitable for a beginners' course with exponentials

I'm currently involved in developing materials for a new UK tier of examination known as Core Maths. The course is designed for 16-18 year olds to further their mathematics education but without taking the traditional A level maths (which is seen as the prerequisite for university)

I would be grateful for any suggestions for lesson ideas or resources that cover

1. Exponentials growth decay in graph or otherwise
2. Introduction to logarithmic scales

The students taking this course are doing so to support their other academic studies. It would appropriate therefore to assume only basic knowledge.

For my part (and to give a flavour of what I'm after) I am making a card sort activity involving the graphs of $y=2^x$, $y=3^x$ and $y=2^{-x}$ etc. Students to compare and contrast formulating generalisations. If you include the source I will make sure the originator is fully accredited.

I'm not gaining financially (the school I work for was selected to develop good practice).

• using the sad earthquakes of this weekend, explaining the Richter scale would be a nice example of logarithmic scale. – Lucas Virgili Apr 26 '15 at 18:54
• @Lucas Virgili That's a great idea. Do you know of any good simple reference material? – Karl Apr 26 '15 at 19:09
• not really :( My only knowledge of it it's the basics as well. Sorry. – Lucas Virgili Apr 26 '15 at 23:37
• Have you checked the Shell Centre? e.g., MARS materials here... – Benjamin Dickman Jul 26 '15 at 21:46
• I have briefly looked into the shell centre thanks. I will take a closer look when I've chance. – Karl Jul 27 '15 at 21:00

Exponential growth or decay shows up everywhere in nature:

2. Diffusion across a membrane (like in osmosis)
4. Dampening (like of a vibrating string/pipe)
5. Attenuation of a signal through a medium (like visibility in water)
6. Uninhibited population growth (like at the start of virus epidemics)

Exponential scales include:

1. Loudness in decibels
2. Octaves and other intervals in music
3. Earthquake energy on the Richter scale
4. Amount of information in bytes in powers of 1024
5. Moore's 'law' (but it is going to fail soon)
6. Acidity/basicity on the pH scale

They also show up in useful procedures:

1. Binary search (guess a number, I'll tell you whether you are high or low on each try)
2. Decimal/binary representation (the number of symbols used compared to the value)
3. Linearization (of suspected power relations)

I think that's more than enough significant real-world applications.

• Thanks. Great answer. Going to start with looking at pH scale. – Karl Jul 24 '15 at 21:38
• Why do you think Moore's law is ready to fail? I've heard this since half micron ic process technology and its continued for decades. – JTP - Apologise to Monica Jul 24 '15 at 21:42
• @JoeTaxpayer: There is a quantum mechanical barrier that cannot be circumvented. The absolute limits are rather tiny, but we almost surely cannot even get anywhere near, so estimated realistic limits are much bigger; see the Wikipedia article for a brief summary. – user21820 Jul 25 '15 at 7:25