Question

One company buys a new bulldozer for $108250. The company depreciates the bulldozer linearly over its useful life of 16 years. Its salvage value at the end of 16 years is $14650.

A) Express the value of the bulldozer, V, as a function of how many years old it is, t. Make sure to use function notation.

Answer 1

`V(t)=108,250-5850t`

Step-by-step explanation:

Let t represent number of years.

We have been given that one company buys a new bulldozer for $108250. Its salvage value at the end of 16 years is $14650.

First of all, we will find depreciation in 16 years by subtracting final value from initial value.

`\text{Depreciation of bulldozer cost in 16 years}=\$108,250-\$14,650`

`\text{Depreciation of bulldozer cost in 16 years}=\$93,600`

Now, we will find depreciation per year for bulldozer by dividing total depreciation value by 16.

`\text{Depreciation per year}=(\$93,600)/(16)`

`\text{Depreciation per year}=\$5850`

The value of bulldozer after t years,
`V(t)`, would be initial value minus depreciation per year as:

`V(t)=108,250-5850t`

Therefore, our required function would be
`V(t)=108,250-5850t`.

Answer 2

To answer the problem above, we make the assumption first that the depreciation is a straight-line method in order to solve for the depreciation rate.
d = (108250 - 14650)/ 16 = 5850
The value of the bulldozer at any time t should be given by the equation,
V = 108250 - 5850t