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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 :

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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

Answer:

[tex]V(t)=108,250-5850t[/tex]

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.

[tex]\text{Depreciation of bulldozer cost in 16 years}=\$108,250-\$14,650[/tex]

[tex]\text{Depreciation of bulldozer cost in 16 years}=\$93,600[/tex]

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

[tex]\text{Depreciation per year}=\frac{\$93,600}{16}[/tex]

[tex]\text{Depreciation per year}=\$5850[/tex]

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

[tex]V(t)=108,250-5850t[/tex]

Therefore, our required function would be [tex]V(t)=108,250-5850t[/tex].

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