Plan. Meeting in the Mac Lab for the first time so that next time (when they have the first exam) won’t be the first time. I hope to have lots of questions that will let us solidify the first month of the semester – estimation, precision, percentages, exposition, common sense. There may be particular questions about inflation.
At the end of the last class I left hanging the question on finding an average annual inflation rate when the 10 year rate was known. I will tackle that today only if there aren’t enough useful summarizing questions from the class.
Another subtle question. In the homework we discovered that the relative error using 1000 bytes per bytes doubles when you use 10^6 bytes per megabyte. That’s counterintuitive (and I got it wrong the first time myself). The reasoning is pretty subtle. How should I deal with questions like this which a few students will appreciate, most tune out?
I think the class went well. The lab setting wasn’t too distracting since we knew each other from the better classroom setting.
Good review on the meaning of “adjusting for inflation” and on relative and absolute change, and on the 1+ trick.
I did one of the homework problems for the first time (it was flagged as [Untested] in the text and discovered that the large increase in private college expenditures per student in a recent decade was actually a decrease when we looked at the inflation adjustment. I think the class liked that.
One student asked how to adjust some number of billions of dollars for inflation when the inflation calculator wouldn’t accept all the digits. Answer: enter 22.1 instead of 22,100,000,000. That was a useful way to reinforce the idea that inflation was a rate, not an amount.
I was able to close with a discussion of the average annual inflation rate when the rate for a decade was 22.6%. Computing (1.0226)^10 showed that dividing the percentage increase by 10 gave an answer that was too large. The analogy: two 10% raises make a 21% raise, not a 20% raise. Then we guessed (1.200)^10, which was too small. I think they all appreciated cut-and-try as a technique that could work in many problems (I said you needed logarithms for this one and we wouldn’t go there.)
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