A truck purchased for $72 000 is depreciated by $4800 per year.
a What is the salvage value of the truck after 3 years?
b After how many years is the salvage value of the truck $38 400?

Let's tackle the problem step by step.

### Given Information:
- Initial value of the truck: $72,000
- Depreciation per year: $4,800

We can write the formula for the salvage value after $ t $ years as:

\[
\text{Salvage Value} = \text{Initial Value} - (\text{Depreciation per year} \times t)
\]

### Part (a): Salvage Value After 3 Years
\[
\text{Salvage Value} = 72,000 - (4,800 \times 3)
\]
\[
\text{Salvage Value} = 72,000 - 14,400 = 57,600
\]

So, the salvage value of the truck after 3 years is **$57,600**.

### Part (b): After How Many Years is the Salvage Value $38,400?
We need to solve for $ t $ when the salvage value is $38,400.

\[
38,400 = 72,000 - (4,800 \times t)
\]
Rearranging the equation:
\[
4,800 \times t = 72,000 - 38,400
\]
\[
4,800 \times t = 33,600
\]
\[
t = \frac{33,600}{4,800} = 7
\]

So, the salvage value of the truck will be **$38,400** after **7 years**.

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Would you like further details on this, or do you have any questions?

Here are 5 related questions to consider:
1. What would be the salvage value after 5 years of depreciation?
2. How would the formula change if depreciation was 10% of the truck's value per year?
3. If the depreciation rate increased to $6,000 per year, how long would it take to reach a salvage value of $30,000?
4. What would be the salvage value after 10 years if the truck depreciated by $3,500 annually?
5. How does changing the depreciation rate affect the time to reach a specific salvage value?

**Tip**: Depreciation can be either linear (as in this example) or based on percentage; understanding both helps with various real-world financial applications.

A truck purchased for $72,000 is depreciated by $4,800 per year. a) What is the salvage value of the truck after 3 years? b) After how many years is the salvage value of the truck $38,400?

Learn how to calculate the salvage value of a truck purchased for $72,000, depreciating by $4,800 annually. Find the salvage value after 3 years and the time required for the value to reach $38,400. This problem demonstrates linear depreciation concepts and algebraic manipulation, ideal for students in Grades 8-10.

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