Suppose that your friend Rhyley has saved $5,000 toward the cost of a car and her parents have agreed to match that amount, dollar for dollar. You learned in your algebra 2 class that the value of a car decreases as time passes. You want to use your knowledge to help your friend buy the best car that she can with the money she has available. Rhyley has narrowed the options down to two different cars, both of which have similar features: Car A Cost: $8,750 Mileage: 89,325 Year of Manufacture: 2015 Decay Factor (average): 12% Car B Cost: $9,995 Mileage: 73,498 Year of Manufacture: 2017 Decay Factor (average): 18%

Suppose that your friend Rhyley has saved $5,000 toward the cost of a car and her parents have agreed to match that amount, dollar for dollar. You learned in your algebra 2 class that the value of a car decreases as time passes. You want to use your knowledge to help your friend buy the best car that she can with the money she has available. Rhyley has narrowed the options down to two different cars, both of which have similar features: Car A Cost: $8,750 Mileage: 89,325 Year of Manufacture: 2015 Decay Factor (average): 12% Car B Cost: $9,995 Mileage: 73,498 Year of Manufacture: 2017 Decay Factor (average): 18%

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

1. Write an exponential decay function in the form f(x)=ab^x for each of Car A and Car B.
Explain how you determined the value of b for each function.

2. Use the Desmos graphing utility to create two graphs; one for each function that you wrote in
question 1. Explain what each axis represents and why you choose the scale you did. You may
also plot these graphs by hand, if you prefer.

3. Look at your graphs from question 2. Explain the value of each y-intercept in context of the
scenario.

Suppose that your friend Rhyley has saved $5,000 toward the cost of a car and her parents have
agreed to match that amount, dollar for dollar. You learned in your algebra 2 class that the value
of a car decreases as time passes. You want to use your knowledge to help your friend buy the
best car that she can with the money she has available. Rhyley has narrowed the options down to
two different cars, both of which have similar features:
Car A
Cost: $8,750
Mileage: 89,325
Year of Manufacture: 2015
Decay Factor (average): 12%
Car B
Cost: $9,995
Mileage: 73,498
Year of Manufacture: 2017
Decay Factor (average): 18%

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