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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![**Depreciation Problem: Calculating the Value of a Depreciating Asset**
**Question:**
Junior bought a work truck for $13,000. The value of his truck will depreciate, or decrease, by 15% each year. Which recursive formula models the value of his truck after each year?
**Answer Choices:**
A.
\[ a_1 = 13,000 \]
\[ a_n = a_{n-1} (1 + 0.15) \]
B.
\[ a_1 = 13,000 \]
\[ a_n = a_{n-1} - 0.15 \]
C.
\[ a_1 = 13,000 \]
\[ a_n = a_{n-1} + 0.15 \]
D.
\[ a_1 = 13,000 \]
\[ a_n = a_{n-1} (1 - 0.15) \]
**Explanation:**
- **Option A:** Suggests the value increases by 15% each year, which is incorrect for depreciation.
- **Option B:** Suggests the value decreases by a constant $0.15 per year, which is not correct as depreciation is a percentage-based decrease.
- **Option C:** Suggests the value increases by a constant $0.15 per year, which is also incorrect.
- **Option D:** Correctly represents a 15% decrease each year. The recursive formula correctly models the value of the truck accounting for a decrease of 15% each year.
For depreciation:
\[ \text{New Value} = \text{Old Value} \times (1 - \text{Depreciation Rate}) \]
Thus,
\[ a_n = a_{n-1} \times (1 - 0.15) \]
Therefore, the correct answer is **Option D**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F65af9c16-2b1a-4650-81ff-ba0e15931f26%2F9da2182c-8019-4857-8d31-f2b4f204a33c%2Fhz1q7l_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Depreciation Problem: Calculating the Value of a Depreciating Asset**
**Question:**
Junior bought a work truck for $13,000. The value of his truck will depreciate, or decrease, by 15% each year. Which recursive formula models the value of his truck after each year?
**Answer Choices:**
A.
\[ a_1 = 13,000 \]
\[ a_n = a_{n-1} (1 + 0.15) \]
B.
\[ a_1 = 13,000 \]
\[ a_n = a_{n-1} - 0.15 \]
C.
\[ a_1 = 13,000 \]
\[ a_n = a_{n-1} + 0.15 \]
D.
\[ a_1 = 13,000 \]
\[ a_n = a_{n-1} (1 - 0.15) \]
**Explanation:**
- **Option A:** Suggests the value increases by 15% each year, which is incorrect for depreciation.
- **Option B:** Suggests the value decreases by a constant $0.15 per year, which is not correct as depreciation is a percentage-based decrease.
- **Option C:** Suggests the value increases by a constant $0.15 per year, which is also incorrect.
- **Option D:** Correctly represents a 15% decrease each year. The recursive formula correctly models the value of the truck accounting for a decrease of 15% each year.
For depreciation:
\[ \text{New Value} = \text{Old Value} \times (1 - \text{Depreciation Rate}) \]
Thus,
\[ a_n = a_{n-1} \times (1 - 0.15) \]
Therefore, the correct answer is **Option D**.
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