The total amount of consumer credit has been increasing steadily in recent years. The following table gives the total outstanding consumer credit​ (in billions of​ dollars). Answer parts​ (a) through​ (e) below.

Year

Consumer

Credit

Year

Consumer

Credit
 
20042004

2210.52210.5

20092009

2557.52557.5

20052005

2303.82303.8

20102010

2643.12643.1

20062006

2437.02437.0

20112011

2759.02759.0

20072007

2540.92540.9

20122012

2924.32924.3

20082008

2597.12597.1

20132013

3099.23099.2

Question content area bottom

Part 1

**a**. 

Find an equation for the least squares​ line, letting x equal the number of years since 

20002000.

The equation is 

Yequals=86.1786.17xplus+1874.761874.76.

​(Use integers or decimals for any numbers in the equation. Round to two decimal places as​ needed.)

Part 2

**b**. 

Based on the answer to part​ (a), at approximately what rate is consumer credit growing per​ year?

The consumer credit is growing about 

​$enter your response here 

billion per year.

​(Round to two decimal places as​ needed.)

### Part 2: Determining the Rate of Growth in Consumer Credit

The equation from Part 1 is given as:

\[
Y = 86.17x + 1874.76
\]

Here, $ Y $ represents the total outstanding consumer credit (in billions of dollars), and $ x $ represents the number of years since 2000.

### Interpretation of the Slope
The slope of the line, $ m = 86.17 $, represents the rate of change of consumer credit with respect to time. In the context of this problem:

- **Slope $ m = 86.17 $**: This means that for each additional year after 2000, the total outstanding consumer credit increases by approximately 86.17 billion dollars.

### Conclusion
Therefore, **the consumer credit is growing at a rate of approximately $86.17 billion per year**.

Would you like to explore how this model can be applied further or discuss other related concepts?

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### Related Questions:
1. How does the slope $ m = 86.17 $ compare with previous trends in consumer credit growth?
2. Can this model be used to predict consumer credit beyond 2013? What limitations might it have?
3. How would a change in the slope impact the predictions for future consumer credit?
4. How would you calculate the predicted consumer credit for the year 2020 using this model?
5. What factors could potentially influence a deviation from this calculated growth rate?

### Tip:
When analyzing the rate of growth in any financial model, it's crucial to consider both historical trends and potential future economic conditions that might alter the growth rate.

Explore how to calculate the rate of growth in consumer credit using linear regression and the least squares method. Understand the equation Y = 86.17x + 1874.76 and learn how each year since 2000 affects the total outstanding consumer credit. Suitable for high school students learning about linear regression in mathematics.

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