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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![**Problem: Calculating Depreciation of a Boat**
You decide to buy a boat that costs $8200. The normal depreciation for such a boat is 14% per year. How much will the boat be worth after 7 years?
**To solve this problem:**
1. **Understand Depreciation:**
- The value of the boat decreases by 14% each year.
2. **Apply the Depreciation Formula:**
- Use the formula for depreciation:
\[
\text{Final Value} = \text{Initial Value} \times (1 - \text{Depreciation Rate})^{\text{Number of Years}}
\]
- In this case:
\[
\text{Final Value} = 8200 \times (1 - 0.14)^7
\]
**Equation:**
\[
\text{Final Value} = 8200 \times (0.86)^7
\]
**Answer:**
\[
\text{Final Value} \approx \$3640.52
\]
After 7 years, the boat will be worth approximately $3640.52.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa93fe523-bbc5-4ded-98ad-9d42c9cf636e%2Fcd6c98fa-1185-413b-9603-3959fd263c0d%2Ffnzcof_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem: Calculating Depreciation of a Boat**
You decide to buy a boat that costs $8200. The normal depreciation for such a boat is 14% per year. How much will the boat be worth after 7 years?
**To solve this problem:**
1. **Understand Depreciation:**
- The value of the boat decreases by 14% each year.
2. **Apply the Depreciation Formula:**
- Use the formula for depreciation:
\[
\text{Final Value} = \text{Initial Value} \times (1 - \text{Depreciation Rate})^{\text{Number of Years}}
\]
- In this case:
\[
\text{Final Value} = 8200 \times (1 - 0.14)^7
\]
**Equation:**
\[
\text{Final Value} = 8200 \times (0.86)^7
\]
**Answer:**
\[
\text{Final Value} \approx \$3640.52
\]
After 7 years, the boat will be worth approximately $3640.52.
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