Drugs, Sex, & Rock-n-Roll

That was the title of today's notes in precalculus in which we were to delve into a revisiting of logarithms. I know, it's REALLY "s, d, & rnr" (as my wise 11th graders kept reminding me), but I thought about the drugs 1st (since my vitamins were sitting on the student desks, and I moved them to under my document camera and thought drugs), then I thought about the population growth model we'd be talking about, and DING, sex .... then it was only a short hop to how we'd also be briefly discussing decibel levels and BOOM, rock-n-roll.

I started class with a cool problem I got at NCTM a long time ago, something to the effect of:

An athlete ingests 16mg of drug at 8am, and has to take a drug test at 1pm. His body metabolizes the drug at a rate of 25% an hour, and to pass the drug test, he can have at most 1mg of drug in his body. Will he pass the drug test? If not then when (hour, minute, second) can he pass? How much could he have taken at 8am to actually pass at 1pm?

I broke it up into parts, and we had good discussions about various things:
* why not be 0mg to pass?
* how do you convert decimal numbers/answers to actual time?
* okay, this may not happen, but think about hospitals and drugs and surgery scenarios.
* what does metabolizing 25%/hour mean?

After this, then we got to sex. I'd looked up the US population as of mid 2011 (311,800,000), and separately found a model for US population, and asked if the model was accurate. That's all I gave them, and had them work things out and back up their reasoning. Good discussions:
* how do they get the models?
* how far off is it when we see the numbers? (% difference)

Then class was almost over, but I'd copied a brief example on how they calculate decibel levels of noise, and I mentioned cilia in the ear and how once it's damaged, it doesn't repair itself and such. Some kids talked about how their dad's or grandfathers were in rock bands or such and had huge hearing loss.

Of course we had a brief review of log rules and such and they did get basic review homework and practice, but it was fun to tease them along.