Picked up where I left off last time — simple vs compound interest. I used the linearexponential spreadsheet rather than writing on the board. Doing it that way I realized again the value in teaching algebra with Excel. That spreadsheet names the cells containing constant values, so the formula for linear growth looks like this
= START + ABSCHANGE *<cell reference>
and the one for exponential growth is
= START * RELCHANGE ^<cell reference>
The class was really amused when I demonstrated by naming a cell “SUSAN”. (There’s no Susan in the class.)
They were also somewhat amused (and perhaps even convinced) by my insistence on their learning how to spell new words – in this case “exponential” (so that I never see the “expodental” that came from one student a long time ago). I told them that the fact that spelling errors jumped off the page to me was (for me) sometimes a curse — preventing me from appreciating the meaning in an otherwise well written well argued piece. But for them spelling errors could cost them a job or a promotion. My suggestions: use a spell checker (of course), show your work to someone who knows how to spell. Marry someone who knows how to spell.
Excel’s what-if capability made it easy to see doubling (growth factor 2, or 100% interest), the fact that exponential growth always catches linear if you wait long enough (change the STEP in the spreadsheet). You can even see that any relative change rate looks like any other if you just rescale – which Excel does for you. The same spreadsheet does depreciation, using a negative absolute change and a relative change less than one.
I said above that Excel makes these things easy. Let me qualify that — perhaps too easy. I know in my bones that “covering” all that material in less than one class period means that much of it left no lasting impression on most of the students. But I think they enjoyed the show — even a magic show is a kind of learning experience.
I had hoped to talk about credit card debt extensively but only just got started. (I couldn’t help but inject some politics – several of the nasty things credit card companies used to be able to do they can’t do any more because of the financial reform package enacted by the last Congress. My students didn’t know anything about that – nor did they vote (many of them) in the last election.)
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