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# Drinking and Driving Activity

Lesson 7 of 11

## 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.

#### Warm-Up

*20 min*

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, ...

#### Resources

*expand content*

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:

- 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.
- Modeling a situation with a mathematical function allows us to predict unknown values
- 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

#### Resources

*expand content*

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- LESSON 1: Properties of Exponents
- LESSON 2: Exponential Equations
- LESSON 3: Logarithms
- LESSON 4: Quiz and Graphing Exponential Functions
- LESSON 5: Multiple Representations of Exponential Functions
- LESSON 6: Quiz and Comparing Linear, Exponential Models
- LESSON 7: Drinking and Driving Activity
- LESSON 8: Exponential Models in the Sciences
- LESSON 9: Exponential Functions in Finance
- LESSON 10: Review Workshop: Exponential Functions and Logarithms
- LESSON 11: Unit Test: Logarithms and Exponential Functions