Plan: exponential growth. Start by recalling the distinction between constant absolute change and constant relative change. The first leads to a straight line. We’ve seen the second in percentage change and the 1+ trick. Compare linear and exponential growth, then go directly to credit card discussion.
— unless there are unanswered homework questions that take precedence.
The good news and the bad news is that I did pretty much everything I’d planned to do. We read the linear vs exponential spreadsheet. It’s more sophisticated than ones they could write, but reading is easier, and valuable. In particular, naming the cells there means that the Excel formulas read just like the ones I write on the board.
One student was particularly intent on learning what negative slopes meant, so we digressed into depreciation. They understood – for a fleeting moment – the analogy (positive vs negative) is to addition as (greater than 1 vs less than 1) is to multiplication. And laughed when I acknowledged that although they understood now they might not in an hour or a day from now. Even in a course where the goal is to teach things that will matter for the next ten years, sometimes understanding is temporary.
We talked about how credit card companies make their money – some from merchants, who willingingly pay for the convenience, some from people who don’t pay their bills in full. 1.65% interest per month is even more than 12*1.65% per year – we worked out (1.065)^12.
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