19 The salvage or depreciated value, $$ V $$, of a new truck purchased for $$ \$ 58,000 $$ is given by the linear function $$ V(t)=58,000 $$ - $$ 4,000 t $$, where $$ t $$ is the time in years between 0 and 10 . What is the correct interpretation of $$ V(3) $$ ? The truck's depreciated value after 5 years is $$ \$ 54,000 $$. The truck's depreciated value after 3 years is $$ \$ 46,000 $$. The truck's depreciated value after 5 years is $$ \$ 42,000 $$. The depreciated value after 3 years is $$ \$ 50,000 $$.

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To find the correct interpretation of $$ V(3) $$, we need to evaluate the function $$ V(t) = 58,000 - 4,000t $$ at $$ t = 3 $$.

Substituting $$ t = 3 $$ into the function:

$$
V(3) = 58,000 - 4,000 \times 3
$$
$$
V(3) = 58,000 - 12,000
$$
$$
V(3) = 46,000
$$

Thus, $$ V(3) $$ represents the truck's depreciated value after 3 years, which is $$ \$ 46,000 $$.

The correct interpretation is:
**The truck's depreciated value after 3 years is $$ \$ 46,000 $$.**
The truck's depreciated value after 3 years is $$ \$ 46,000 $$.

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