Question

Depreciation is the decrease or loss in value of an item due to age, wear, or market conditions. We usually consider depreciation on expensive items like cars. Businesses use depreciation as a loss when calculating their income and taxes. One company buys a new bulldozer for $137750. The company depreciates the bulldozer linearly over its useful life of 22 years. Its salvage value at the end of 22 years is $16750. 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. B) The value of the bulldozer after 3 years is $

Answer 1

Answer:

A) $V(t) = 137750-5500t$

B) The value of bulldozer after 3 years is $121250

Step-by-step explanation:

We are given the following in the question:

Cost of bulldozer = $137750

The value of bulldozer depreciates linearly.

A) Let V(t) be the linear function that gives the depreciated value of bulldozer after t years. Then, we can write:

$V(t) = a +bt$

Cost of new bulldozer =  $137750

$V(0) =137750\\a + b(0) = 137750\\\Rightarrow a = 137750$

Value of bulldozer at the end of 22 years = $16750

$V(22) =16750\\a + b(22) = 16750\\\Rightarrow 137750 + 22b = 16750\\\\\Rightarrow b = \dfrac{16750-137750}{22} =-5500$

Thus, the value of bulldozer is given by the function V(t)

$V(t) = 137750-5500t$

where t is time in years.

B) Value of bulldozer after 3 years

We put t = 3 in the equation.

$V(3) = 137750-5500(3)=121250$

Thus, the value of bulldozer after 3 years is $121250