We usually teach students all the rules for working with exponents after we teach the basic definition. I don't think I start teaching anything real world until I get to the higher level maths when I teach radioactive decay, population growth and decline, and compound interest. But what about working it in with the other classes? How do you do that? What are some ways exponents are used in real life that we could easily implement in other math classes?
Most of the sites I found that give information on uses in real life only give no more than 4 or 5 examples and even then the examples are just a mention such as exponents are used to determine the spread of disease but its just a mention.
If you go to this site, it has tons of examples of where exponents are used in real life ranging from computers to the size of silicon atoms. Each example includes details on the way the exponents are used and includes a visual illustrating the example. This site even includes an activity for making an exponential decay graph using M & M's. Most students love doing any type of activity using candy, especially if they know they can eat it when they are done. At the end, there is a link to a slide presentation you can use in your classroom which contains the same material. This site is one of the more thorough ones' I've seen.
It has so many examples, the teacher could assign a topic from the presentation to a pair of students who could further research the topic and then the groups could prepare two to three slides in the class presentation. For instance, the author mentioned the pH scale uses exponents. I check it out and yes it does indeed. It actually looks like its more likely a negative exponent because the pH of one means 0.1, a pH of two is 0.01 etc.
The slide show makes a good starting point for an introduction to the real world uses for exponents. If you aren't sure how to teach a unit on exponents or what a student should know there is a lovely mind map at this blog. Although it is focused on junior high, it does have a great layout to see what students should know by the time they hit high school and gives an idea of what to review.
I'm off to do some planning.