2. You decide to buy a boat that costs $8200. The normal depreciation 14% per year. How much will the boat be worth after 7 years? Eguation:

Algebra and Trigonometry (6th Edition)
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Author:Robert F. Blitzer
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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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.
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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