Plan: doubling times, exponential decay, half lives.
Start with “If you invest $1000 at 5% annual interest how long does it take to double your money?” – group work, no instructions. Perhaps ask for “how might you go about this?” in advance? I’d rather not. The whole point of the course is that they shouldn’t be frightened by brand new qr questions.
I did (start with that). The class came up with several methods.
- Compute 1000*1.05 and continue multiplying by 1.05 until you reach 2000 – some with a calculator, some by opening a brand new spreadsheet
- Solve 1000*10.5^? = 2000 by experiment.
- Google “double an investment” – find a calculator that does the work for you.
I was pleased with the exercise. Most of the class was able to find a method and a solution. I did note that no one chose to open the exponential growth spreadsheet we’d played with last class.
The google search led to the Rule of 70 (or 72, depending) which we explored. I asked who needed/wanted to know why it worked, rather than just that it worked. Only a few. And that’s OK. There’s no need to understand all your tools. (Do you know how your computer or your car works, under the hood?) I said you could find out why the rule of 70 if you took calculus. I think I could explain it without calculus in an hour to someone who really cared, but they probably wouldn’t remember the explanation for more than a few minutes. The natural log of 2 is 0.6931, which is just about 0.7.
We worked the exercise in the book that asks for qualitative answers — which of these dependencies is exponential, which linear? Some exponential decrease came up along the way, which motivated the segue into exponential decrease. We started with depreciation, which people understood, then hurriedly did half lives, which was harder. I will assign some half life problems.
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