Probably there is a very easy explanation that Alice () or some other math teacher can shed light on, but I'm having trouble with how to explain part of this problem. The problem is: From 2000 to 2001, median home prices in Austin, TX rose an average of 7.2% per year. Find the MONTHLY percent increase in the value of the home during this time. So I understand the way to do it is V=a(1.072)^t. Then to get the monthly rate you re-write this as V=a(1.072^(1/12))^(12t). You get V=a(.0058)^12t, or a .58% increase. (This is the correct answer, of course, and I checked it with the book.) I struggle with explaining to the kids why you can't just do 7.2/12 to get a .6% increase. (For this particular problem, it comes out really close just doing that, but in most of the other problems, the answers are drastically different.) I'm thinking it has to do with the fact that t is in the exponent and it's not a linear model---the percent is building off of the previous month. I just lack a clear explanation to give the kids of this. How would you explain it. Thanks!!

I'm not a math teacher, but to help them see why they can't just divide by 12, could you relate it to compounded interest?

The reason is because of compound interest. The number of dollars the homes increased in December was much greater than the number of dollars increased in January, because the actual value that you're taking a percentage of is so much higher. So that's why the easier cut-it-into-twelths system doesn't work. You're still doing Principal(rate)(time).

I would work backwards and first have my students create a visual showing the value of a particular house expontially increasing each month so they can visually see that it's not just the percentage divided by 12.

Next month = this month * rate. Next next month = next month * rate. Next next month = (this month * rate ) * rate You can see from this pattern that rate is the only repeating term, and so we get This month * (rate)^t

Do your best to explain it but chalk this problem down as one you need to skip next year. It's a bad problem since the answer from the wrong and write way are too close.