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Let's analyze and solve the problem in your image step by step.

### Part A:
The company bought the bulldozer for $100,850 and will depreciate its value linearly over 16 years, with a salvage value of $16,850 after 16 years.

We can model the value of the bulldozer $ V(t) $, where $ t $ is the number of years after purchase, using the formula for linear depreciation:
\[
V(t) = V_0 - \text{(depreciation rate)} \times t
\]
Where:
- $ V_0 = 100,850 $ (initial value)
- Depreciation rate = $ \frac{100850 - 16850}{16} = \frac{84000}{16} = 5250 $

So the function becomes:
\[
V(t) = 100850 - 5250 \times t
\]
Thus, the value of the bulldozer as a function of $ t $ is:
\[
V(t) = 100850 - 5250t
\]

### Part B:
To find the value of the bulldozer after 12 years, substitute $ t = 12 $ into the function:
\[
V(12) = 100850 - 5250 \times 12
\]
\[
V(12) = 100850 - 63000 = 37850
\]

Thus, the value of the bulldozer after 12 years is **$37,850**.

---

Would you like more details or have any questions? Here are 5 related questions for practice:

1. What will be the value of the bulldozer after 8 years?
2. How long will it take for the bulldozer to depreciate to $20,000?
3. If the salvage value were $25,000 instead of $16,850, how would the depreciation rate change?
4. Can you rewrite the depreciation function if the bulldozer had a lifespan of 20 years instead of 16?
5. How much value does the bulldozer lose per year, and how can you verify that?

### Tip:
Linear depreciation is often modeled by subtracting a constant amount each year. To handle problems like these, always find the annual depreciation rate by dividing the total depreciation by the useful life of the item.

One company buys a new bulldozer for $100,850. The company depreciates the bulldozer linearly over its useful life of 16 years. Its salvage value at the end of 16 years is $16,850. Express the value of the bulldozer, V, as a function of how many years old it is, t. Also, find the value of the bulldozer after 12 years.

Learn how to calculate the value of a bulldozer using a linear depreciation model. This example involves a bulldozer purchased for $100,850, with a salvage value of $16,850 after 16 years. Discover how to express the value of the bulldozer as a function of time and determine its value after 12 years.

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