The value of a new car purchased for $20,000 decreases by 10% per year. Write an exponential decay model for the value of the car. Use the model to estimate the value after 4 years.

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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18. The value of a new car purchased for $20,000
decreases by 10% per year. Write an exponential
decay model for the value of the car. Use the
model to estimate the value after 4 years.
Transcribed Image Text:work to earn full credit! 18. The value of a new car purchased for $20,000 decreases by 10% per year. Write an exponential decay model for the value of the car. Use the model to estimate the value after 4 years.
Expert Solution
Step 1

Given data:

The given value of the car is a=$20,000.

The rate at which the value of the car decreases is r=10%=0.1.

The expression for the exponential decay model  is,

x=a1-rt

Substitute the given values in the above expression.

x=20,0001-0.1t=20,0000.9t...................(I)

 

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