Abstract: Alcohol is one of the new experiences most of the 15 -16 year old teenagers have. Thus this topic is important to them and is motivating enough having more insight.
Investigating Blood Alcohol Concentration (BAC) leads to the mathematical issue of limited and logistic growth and decay models and the risk of alcohol as well. Additional aims of these lecture s are using GeoGebra with the “Two Variable Regression Analysis” at the spreadsheet view. Further having the ability to discuss statements about alcohol from the mathematical point of view written in the literature and the world-wide-web.
Overview
Teachers
Period of Time
Type of School
Age of Students
Number of Students/Class
Special Requirements
Andreas Kiener
3 hours
Gymnasium
15 -16
24
Special computer classroom with 24 Computers, Beamer
Web address to materials
Worksheet: http://www.geogebratube.org/student/m45913
National Institute on Alcohol Abuse and Alcoholism: http://pubs.niaaa.nih.gov/publications/aa35.htm
Mayo Clinic: http://www.mayomedicallaboratories.com/articles/drugbook/alcohol.html
WIKI: http://en.wikipedia.org/wiki/Blood_alcohol_concentration

Comparing linear and exponential decay
Investigating observed BAC
Description of Lesson / Project
The sequence was split into three lessons. The first lesson was about calculating the BAC of several drinks at a party and comparing the values with physiological effects.
The second lesson was about the recursive equation of linear, exponential and logistic decay. Reading about the decay of BAC it is obvious that there is no clear distinction of
BAC decay between per mill-points and per mill. The first expression leads to a linear decay the second one to an exponential decay.
The spreadsheet view of GeoGebra helps to investigate this situation by transforming the linear recursive equation and the recursive exponential equation to the respective spreadsheet formula. The “Two Variable Regression Analysis” plots the explicit functions.

Finally observed BAC was investigated. Fortunately there is a plot available about the pharmacokinetics of ethanol after oral administration of ethanol to eight normal weight male volunteers. Each subject got a different amount of ethanol in the fasting state. This plot was imported as a picture to GeoGebra, scaled and aligned to the axes.
Within this prepared worksheet the students had just to set points at the imported plot according to the measured points. T he „Two Variable Regression Analysis“ shows the dialog for choosing the model of growth and decay. Right now it's up to the students to experiment with all available models in order to find the proper one. At the bottom of this dialog they will find the explicit equation for the chosen model. It's possible to bring the solution back to the graphics view.
Our Experiences
Working with computer is seen as a variation of daily routine. With the prepared worksheet each student got a result even with less skill. Thus it was motivating too. They described it as easy and the visualization with GeoGebra helped them for better understanding. The students were astonished that mathematics describes even alcoholic blood concentration. They see that mathematics could be important in future, because it's inside everywhere.
From the teachers point of view they worked more independently and more concentrated.
Some had problems with handling computers generally.
Further Activities
A plot found on Wikipedia describing the Probability of car accidences in dependence of
BAC could be analysed in the same way.