4.9: Saving Green

INTRODUCTION

In this collaboration, you continue to examine the financial impact of buying a hybrid car versus a non-hybrid car. In Collaboration 4.8, you created a linear model to represent the yearly savings in gas due to driving a fuel-efficient car. In this collaboration, you use what you have learned about compound interest to examine the savings from a different point of view—the person who did not buy the fuel-efficient car. In this scenario, the savings from buying a less expensive vehicle is placed in a bank to earn interest.

Note that the suggested timeline for this collaboration indicates that a lot of personal responsibility is placed on your groups. Unlike previous collaborations, there are not a lot of preparatory questions in the problem situation. You are expected to rely on your group and the work done previously in the course to work through this collaboration. After the initial discussion to make sure the problem situation is understood and reasonable assumptions have been made, you will create, analyze, and use your savings model.

Your instructor will analyze your collaboration work and provide you with detailed feedback.

There are no Preparation or Exercise assignments related to this collaboration.

SPECIFIC OBJECTIVES

By the end of this collaboration, you should understand that

• mathematical modeling or quantitative reasoning can be used to help make personal financial decisions.

By the end of this collaboration, you should be able to

• identify missing information.
• demonstrate an ability to determine reasonable values for missing information.
• construct a linear model of a savings scenario.
• describe–in words and graphs–the effect changes in assumptions have on linear models.

PROBLEM SITUATION: COMPARING THE COST OF CARS (A CONTINUATION OF COLLABORATION 4.8)

Suppose you buy the non-hybrid Accord. Since this car is cheaper, you have already saved some money compared with someone who bought the hybrid car. If these savings are invested in a savings account that earns interest, they could continue to grow over time.

(1) Create an algebraic model (equation) for the amount of savings over time. Determine reasonable values for any missing information and define all variables.

(2) Produce a graph of your model and label your axes appropriately. Note: If completing this problem online, follow the instructions given online to create your graph.

(3) Now that you have invested time creating and studying two savings models (you created one of these models in Collaboration 4.8), you want to share your analysis with your peers. Suppose you have the opportunity to submit one paragraph on a blog for college students. Write a paragraph that compares the gasoline costs associated with gas-powered and hybrid vehicles. Your paragraph should include a final recommendation on whether someone should buy a gas-powered or hybrid vehicle.

MAKING CONNECTIONS

Record the important mathematical ideas from the discussion.