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.
\begin{tabular}{|c|c|c|c|}
\hline Year & $\begin{array}{c}\text { Consumer } \\
\text { Credit }\end{array}$ & Year & $\begin{array}{c}\text { Consumer } \\
\text { Credit }\end{array}$ \\
\hline 2003 & 2219.5 & 2008 & 2553.5 \\
\hline 2004 & 2319.8 & 2009 & 2645.1 \\
\hline 2005 & 2415.0 & 2010 & 2756.0 \\
\hline 2006 & 2551.9 & 2011 & 2926.3 \\
\hline 2007 & 2595.1 & 2012 & 3099.2 \\
\hline
\end{tabular}
a. Find an equation for the least squares line, letting $x$ equal the number of years since 2001.
The equation is $Y=85.49 \mathrm{x}+2052.46$.
(Use integers or decimals for any numbers in the equation. Round to two decimal places as needed.)
b. Based on the answer to part (a), at approximately what rate is consumer credit growing per year?
The consumer credit is growing about $\$ 85.49$ billion per year.
(Round to two decimal places as needed.)
c. Use the result from part (a) to predict the amount of consumer credit in the year 2015.
The amount of consumer credit in the year 2015 will be $\$ 3249^{\top}$ billion.
(Round to the nearest whole number.)
d. If this trend continues linearly, in what year will the total debt first exceed $\$ 4000$ billion?
If this trend continues linearly, in the year , total debt will first exceed $\$ 4000$ billion.
(Round up to the nearest whole number.)
Answer
Final Answer: If this trend continues linearly, in the year \(\boxed{2024}\), total debt will first exceed $4000 billion.
Step 1 ：Given the equation of the least squares line as \(Y=85.49x+2052.46\), where \(x\) is the number of years since 2001 and \(Y\) is the consumer credit in billions of dollars.
Step 2 ：We need to find the year when the total debt first exceeds $4000 billion. This means we need to solve the equation \(85.49x+2052.46 = 4000\) for \(x\).
Step 3 ：Solving the equation gives \(x = 22.780910047958827\).
Step 4 ：Adding this to 2001 to get the year, we get the year as 2024.
Step 5 ：Final Answer: If this trend continues linearly, in the year \(\boxed{2024}\), total debt will first exceed $4000 billion.
