Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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11. in 2011 dollars, the price is how much
![### Calculating Inflation-Adjusted Prices Using the Consumer Price Index (CPI)
**Problem:** Suppose a particular car cost $1900 in 1990. What was the price in 2011 dollars? Assume that all prices have risen at the same rate as the CPI.
**Instruction:** Round to the nearest dollar as needed.
---
**Solution:**
To find the price of the car in 2011 dollars, we need to use the Consumer Price Index (CPI) data provided in the table.
**Step-by-Step Calculation:**
1. **Identify the CPI for the relevant years:**
- CPI for 1990: 130.7
- CPI for 2011: 224.9
2. **Adjust the 1990 price to 2011 dollars:**
The formula to adjust the price is:
\[
\text{Price in 2011 dollars} = \text{Price in 1990 dollars} \times \left( \frac{\text{CPI in 2011}}{\text{CPI in 1990}} \right)
\]
3. **Insert the values:**
\[
\text{Price in 2011 dollars} = 1900 \times \left( \frac{224.9}{130.7} \right)
\]
4. **Calculate the result:**
\[
\text{Price in 2011 dollars} \approx 1900 \times 1.7222 \approx 3272.18
\]
5. **Round the result:**
\[
\text{In 2011 dollars, the price is \$3272}
\]
**Conclusion:**
- In 2011 dollars, the price of the car is **$3272**.
---
**Table Explanation:**
The table on the right side of the image shows the Average Annual Consumer Price Index (CPI) for each year from 1981 to 2020. The base period used for the CPI is 1982–1984, set to an index value of 100. The CPI values indicate how much the price level has changed relative to the base period.
For example:
- The CPI for 1981 is 90.9, which means that the price level in 1981 was 90.9% of the base period.
- The CPI for](https://content.bartleby.com/qna-images/question/d357b89a-d63d-400d-a75c-5f74a0421e19/2f06d31d-52e5-413f-90d8-a3bb088c4aaf/1vxybxl_processed.png)
Transcribed Image Text:### Calculating Inflation-Adjusted Prices Using the Consumer Price Index (CPI)
**Problem:** Suppose a particular car cost $1900 in 1990. What was the price in 2011 dollars? Assume that all prices have risen at the same rate as the CPI.
**Instruction:** Round to the nearest dollar as needed.
---
**Solution:**
To find the price of the car in 2011 dollars, we need to use the Consumer Price Index (CPI) data provided in the table.
**Step-by-Step Calculation:**
1. **Identify the CPI for the relevant years:**
- CPI for 1990: 130.7
- CPI for 2011: 224.9
2. **Adjust the 1990 price to 2011 dollars:**
The formula to adjust the price is:
\[
\text{Price in 2011 dollars} = \text{Price in 1990 dollars} \times \left( \frac{\text{CPI in 2011}}{\text{CPI in 1990}} \right)
\]
3. **Insert the values:**
\[
\text{Price in 2011 dollars} = 1900 \times \left( \frac{224.9}{130.7} \right)
\]
4. **Calculate the result:**
\[
\text{Price in 2011 dollars} \approx 1900 \times 1.7222 \approx 3272.18
\]
5. **Round the result:**
\[
\text{In 2011 dollars, the price is \$3272}
\]
**Conclusion:**
- In 2011 dollars, the price of the car is **$3272**.
---
**Table Explanation:**
The table on the right side of the image shows the Average Annual Consumer Price Index (CPI) for each year from 1981 to 2020. The base period used for the CPI is 1982–1984, set to an index value of 100. The CPI values indicate how much the price level has changed relative to the base period.
For example:
- The CPI for 1981 is 90.9, which means that the price level in 1981 was 90.9% of the base period.
- The CPI for
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