Thursday, January 20, 2011

An Omen of Sorts

Me to Kid 1: "I had a terrible nightmare last night, and you were in it."

Kid 1: "Really? What was it about?"

Me: "I was giving a bunch of you a ride home and we got into a horrible accident!"

Kid 2: "You know what it means when a math teacher has a dream about you, right?"

Us: "????"

Kid 2: "You're going to give birth to the antichrist."

Sunday, January 16, 2011

Megan Golding is My Hero

Not just for making this crazy-fun project overlaying triangle concurrencies on a school map so that they could be clues for a treasure hunt, but blogging it up so other teachers can hit the ground running. Fantastic use of sketchpad, great game mechanics - she and her colleagues really thought of everything and knocked it out of the park. This is why teachers blog, so the next time someone asks, send them there. :-)

Wednesday, January 5, 2011

e is a Slippery Little Devil

Can someone please explain this to me in a few sentences that make sense, without calculus?

If we start with P, increase it at a rate of r, compounded n times per time period for t time periods, we end up with

$P(1+\frac{r}{n})^{nt}$

If we compound it more and more frequently to the point where we're compounding it all the time, we're basically doing... (I know this is not rigorous. I'm sorry. I'm trying to make this graspable to any old 16 year old. Not just the future engineers etc.)

$P(1+\frac{r}{\infty})^{\infty t}$

And since

$e=(1+\frac{1}{\infty})^\infty$

(Again, I realize this would make a real mathematician bleed from the eyeballs. Sorry sorry sorry.)

That means we can replace part of our percent change equation with e, and calculate continuous growth with

$Pe^{rt}$

To recap:

My question is, why is r in the exponent now? I don't get that.