Sure, let's break down the solution step-by-step and create the complete table as needed.
### Step-by-Step Solution:
1. Initial Value of the Car (Time = 0 years):
The car's initial value is \[tex]$32,000 or 32 (thousands).
2. Value After 1 Year:
Each year, the car retains \( 85\% \) of its previous year's value. To find the value after 1 year, multiply the initial value by 0.85.
\[
32 \times 0.85 = 27.2
\]
3. Value After 2 Years:
To find the car's value after 2 years, multiply the value after 1 year by 0.85.
\[
27.2 \times 0.85 = 23.12
\]
4. Value After 3 Years:
To find the car's value after 3 years, multiply the value after 2 years by 0.85.
\[
23.12 \times 0.85 = 19.652
\]
### Summary Table:
Here is the completed table showing the car's value at the start and for each year up to 3 years.
\begin{tabular}{|c|c|}
\hline
\textbf{Time (Years)} & \textbf{Value (Thousands)} \\
\hline
0 & 32.0 \\
\hline
1 & 27.2 \\
\hline
2 & 23.12 \\
\hline
3 & 19.652 \\
\hline
\end{tabular}
So, the car's value declines over the years as follows: \$[/tex]32,000 at the start, \[tex]$27,200 after 1 year, \$[/tex]23,120 after 2 years, and \$19,652 after 3 years.
Note: In practice, values in financial calculations are often rounded to two decimal places. The slight variations you see (such as 23.119999999999997 instead of 23.12) are results of floating-point arithmetic precision limits in computing.
