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 $101250. The company depreciates the bulldozer linearly over its useful life of 15
years. Its salvage value at the end of 15 years is $15000.
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 8 years is $
PLEASE HELP ASAP

Answer 1

Part A)
`V(t)=-5,750t+101,250`

Part B)
`\$55,250`

Explanation:

Part A) Express the value of the bulldozer, V, as a function of how many years old it is, t.

Let

V ----> the value of the bulldozer (dependent variable or output value)

t ----> the number of years (independent variable or input value)

we know that

The linear function in slope intercept form is equal to

`V(t)=mt+b`

we have the ordered pairs

(0,101,250) and (15,15,000)

Find the slope

The formula to calculate the slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

substitute

`m=(15,000-101,250)/(15-0)`

`m=-\$5,750\ per\ year` ----> is negative because is a decreasing function

The value of b is the initial value

so

`b=\$101,250`

substitute

`V(t)=-5,750t+101,250`

Part B) The value of the bulldozer after 8 years is

For t=8 years

substitute the value of t in the linear equation

`V(t)=-5,750(8)+101,250=\$55,250`