Cynthia Lanius


Fun and Sun

The Green family is planning a one-week vacation in Florida and needs to rent a car while there. They researched and found the following options.  

*Weekly Rate 1   $329 per week, unlimited mileage.
*Weekly Rate 2  $219 per week, plus 12 cents per mile.
*Partial week charged at a full week's price.
**Daily Rate 1   $50 per day, unlimited mileage.
**Daily Rate 2   $40 per day plus 3 cents per mile.
**Partial days charged at a full day's price.

The Greens don't know exactly how far they will drive but estimate that it will be between 500 and 1000 miles. They must decide which plan to choose. Explore the four options below.


Things to Do

Make a Table (Offline)

Make a Graph (Offline)

Analyze the Graph

    1. Each graph contains six points. Is it appropriate to connect the points on the graphs to make lines? Explain why or why not.
    2. Do all of the points of each graph lie on a straight line? What is a function called that has a graph which is a straight line?
    3. Which of the lines is steepest? What is the slope of that line? Which of the functions grows at the fastest rate? Which of the functions grows at the slowest rate? What is its slope ?
    4. If you extend the lines through the y axis, would any of the lines go through the origin? Explain why or why not.
    5. What is significant about the points where the graphs intersect?

Write the Functions

    Write the Total Week's Rental Car Cost as a function of the Number of Miles Driven for each of the options.

Write a Paragraph

Extension 1

Extension 2

Check here for Teachers' Notes

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