# Drinking and Driving Activity

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## Objective

SWBAT Use and exponential model to predict the probability of getting into a car accident as a function of the number of alcoholic beverages consumed.

#### Big Idea

Exponential functions have many applications. One health-related application is the probability of getting into an accident as a function of alcoholic beverages consumed.

## Warm-Up

20 minutes

Exponential functions have a connection to geometric sequences and series, but it is not always clear to students why we study them as two separate topics. For the lesson's warm-up I ask students to answer some questions about geometric functions, some questions about geometric functions.  When they have completed these questions, I spend time discussing the connection between geometric sequences and exponential functions  The most important point I try to drive home is that geometric sequences ARE special exponential functions.  They are geometric functions with a domain restriction of x = 1, 2, 3, ...

## Drinking and Driving Activity

60 minutes

For the Drinking and Driving Activity, students will need an internet-enabled device, a graphing calculator and a pencil.

The goal of the activity is threefold:

1. I want my students to leave the activity with an understanding that each drink they consume increases their probability of having an accident by more than the previous drink.
2. Modeling a situation with a mathematical function allows us to predict unknown values
3. Exponential growth in this situation means that things are getting worse and worse!

The day before this activity, I select groups of 3 students that will work together.  They will receive a group grade for this work, so its important that I arrange students in groups that will participate equally.  I also arrange students so that there is sure to be at least one student in each group with easy internet access.  I arrange the groups on a powerpoint slide so that I can show the slide to students when I ready for them to move.

I start the activity by introducing the idea of probability of an accident.  We talk about what factors affect the likelihood of getting into a car accident.  Because many of my algebra 2 students are in drivers ed, this is a topic that they have been thinking about recently.  The topic of alcohol generally comes up in this conversation, but if it did not, I would steer the conversation in that direction.  At this point I introduce the activity, writing the exponential function introduced in the activity on the board and discussing some of its features. We examine

• the y-intercept and what it means
• whether the function is always increasing, always decreasing or sometimes increasing and sometimes decreasing
• the domain and what it means
• the range and what it means

After we have examined the function in this way, students are ready to jump in because the activity is laid out in a step-y-step way in the document Drinking and Driving Activity.docx