To determine the value of the truck after 3 years, given that it depreciates by 9% each year from its initial value of \[tex]$32,000, we will follow these steps:
1. Calculate the value after the first year:
We start with the initial value of the truck, which is \$[/tex]32,000. Depreciation decreases the value by 9%, so the value remaining after the first year can be calculated as:
[tex]\[
\text{Value after 1 year} = 32000 \times (1 - 0.09)
\][/tex]
Simplifying this expression:
[tex]\[
\text{Value after 1 year} = 32000 \times 0.91
\][/tex]
[tex]\[
\text{Value after 1 year} = 29120.0
\][/tex]
2. Calculate the value after the second year:
Now we take the value after the first year's depreciation, \[tex]$29,120, and apply another 9% depreciation for the second year:
\[
\text{Value after 2 years} = 29120 \times (1 - 0.09)
\]
Simplifying this calculation:
\[
\text{Value after 2 years} = 29120 \times 0.91
\]
\[
\text{Value after 2 years} = 26499.2
\]
3. Calculate the value after the third year:
Finally, we take the value after the second year's depreciation, \$[/tex]26,499.20, and apply a 9% depreciation for the third year:
[tex]\[
\text{Value after 3 years} = 26499.2 \times (1 - 0.09)
\][/tex]
Simplifying this result:
[tex]\[
\text{Value after 3 years} = 26499.2 \times 0.91
\][/tex]
[tex]\[
\text{Value after 3 years} = 24114.272
\][/tex]
Thus, the value of the truck after 3 years, considering a depreciation rate of 9% per year, will be \[tex]$24,114.27, which can be rounded to the nearest dollar, giving us:
\(\boxed{24114}\)
So, the correct answer is:
\[
\$[/tex] 24,114
\]
