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.