Ed's new car has a value of $23,500, but it is expected to depreciate at a rate of 7.5% per year. If you were to write an exponential decay function to represent this situation, what would the initial value be? O 23,500 O 107.5 O 92.5 O 7.5

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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**Understanding Exponential Decay in Car Depreciation**

Ed's new car has a value of $23,500, but it is expected to depreciate at a rate of 7.5% per year. If you were to write an exponential decay function to represent this situation, what would the initial value be?

**Multiple Choice Options:**

- ○ 23,500
- ○ 107.5
- ○ 92.5
- ○ 7.5

Explanation:
In the context of exponential decay, the initial value in this scenario refers to the starting value of Ed’s car before any depreciation occurs. 

### Understanding the Initial Value:
When dealing with exponential decay, which can be represented by the formula \( V(t) = V_0 \times (1 - r)^t \), where:
- \( V(t) \) is the value of the car at time \( t \).
- \( V_0 \) is the initial value (the value of the car when \( t = 0 \)).
- \( r \) is the rate of depreciation.
- \( t \) is the time in years.

Here, the initial value \( V_0 \) is simply the original purchase price of the car, which is $23,500.

Hence, the correct answer is:
- ○ 23,500

No graphs or diagrams are present in this particular section of the educational text.
Transcribed Image Text:**Understanding Exponential Decay in Car Depreciation** Ed's new car has a value of $23,500, but it is expected to depreciate at a rate of 7.5% per year. If you were to write an exponential decay function to represent this situation, what would the initial value be? **Multiple Choice Options:** - ○ 23,500 - ○ 107.5 - ○ 92.5 - ○ 7.5 Explanation: In the context of exponential decay, the initial value in this scenario refers to the starting value of Ed’s car before any depreciation occurs. ### Understanding the Initial Value: When dealing with exponential decay, which can be represented by the formula \( V(t) = V_0 \times (1 - r)^t \), where: - \( V(t) \) is the value of the car at time \( t \). - \( V_0 \) is the initial value (the value of the car when \( t = 0 \)). - \( r \) is the rate of depreciation. - \( t \) is the time in years. Here, the initial value \( V_0 \) is simply the original purchase price of the car, which is $23,500. Hence, the correct answer is: - ○ 23,500 No graphs or diagrams are present in this particular section of the educational text.
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