Question
Make sure you copy every problem with detailed steps into your math notebook. This counts as a formative grade which is \( 23.2 \% \) of your grade. 1 Multiple Choice 10 points Carmen buys a car for \( \$ 28,000 \). The vehicle depreciates by \( 16 \% \) each year. Which of the following is the decay factor representing the car's value every year? 16 0.84 1.84 0.16
Ask by Sullivan Montgomery. in the United States
Jan 23,2025
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Tutor-Verified Answer
Answer
The decay factor is **0.84**.
Solution
Sure, let's break down the problem step by step to understand how to determine the decay factor representing the car's value each year.
---
### **Problem Statement:**
Carmen buys a car for **\$28,000**. The vehicle depreciates by **16%** each year. Which of the following is the decay factor representing the car's value every year?
**Options:**
1. 16
2. 0.84
3. 1.84
4. 0.16
---
### **Understanding Depreciation:**
Depreciation refers to the decrease in the value of an asset over time. In this case, the car loses 16% of its value each year.
### **Decay Factor:**
The **decay factor** is the multiplier that represents the remaining value of the asset after depreciation. It is calculated as:
\[
\text{Decay Factor} = 1 - \text{Depreciation Rate}
\]
Where the depreciation rate is expressed as a decimal.
### **Calculating the Decay Factor:**
1. **Convert the Depreciation Rate to Decimal:**
\[
16\% = \frac{16}{100} = 0.16
\]
2. **Subtract the Depreciation Rate from 1:**
\[
\text{Decay Factor} = 1 - 0.16 = 0.84
\]
### **Interpreting the Decay Factor:**
A decay factor of **0.84** means that each year, the car retains **84%** of its value from the previous year.
### **Verification with Options:**
Let's match our calculated decay factor with the provided options:
1. **16:** This is the depreciation rate, not the decay factor.
2. **0.84:** **This matches our calculated decay factor.**
3. **1.84:** This would imply the car's value is increasing by 84%, which contradicts depreciation.
4. **0.16:** This represents the depreciation rate, not the decay factor.
---
### **Conclusion:**
The correct decay factor representing the car's value every year is **0.84**.
**Answer:** **0.84**
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To determine the decay factor, you need to consider the percentage of value the car retains after depreciation. Since the car depreciates by \( 16\% \) each year, it retains \( 100\% - 16\% = 84\% \) of its value. To express this as a decimal, \( 84\% \) equals \( 0.84 \). Thus, the decay factor representing the car's value every year is \( 0.84 \). When dealing with depreciation problems like this, a common mistake is to confuse the decay factor with the rate of depreciation itself. Remember, the decay factor is what remains after the depreciation is applied, so always subtract the percentage from 100% before converting to a decimal for accurate calculations!
