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 $140050. The company depreciates the bulldozer linearly over its useful life of 25 years. Its salvage value at the end of 25 years is $12550.
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 16 years is $.
Since you claim that the depreciation is linear, (not realistic), let's express the
given data as ordered pairs in the form (years, value), that is,
(0,140050) and (25,12550)
slope = (12550-140050)/(25-0) = -5100
and since the point (0,140050) behaves like the y-intercept in y = mx + b
we have:
value = -5100t + 140050
so when t = 10 , value = .....
I will leave it up to you to state my solution in the way they want.
A) Let's denote the value of the bulldozer as V and the number of years old as t. Since the bulldozer depreciates linearly over its useful life, we can express the value of the bulldozer as a linear function of the number of years.
The starting value of the bulldozer is $140050 and its salvage value at the end of 25 years is $12550. The useful life of the bulldozer is 25 years.
To find the rate of depreciation per year, we can calculate the change in value per year:
Change in value = Starting value - Salvage value
Change in value = $140050 - $12550
Change in value = $127500
The rate of depreciation per year is:
Rate of depreciation per year = Change in value / Useful life
Rate of depreciation per year = $127500 / 25
Rate of depreciation per year = $5100
Now, we can express the value of the bulldozer, V, as a function of the number of years, t:
V(t) = Starting value - Rate of depreciation per year * t
V(t) = $140050 - $5100t
B) To find the value of the bulldozer after 16 years, we can substitute t = 16 into the function we found in part A):
V(16) = $140050 - $5100 * 16
V(16) = $140050 - $81600
V(16) = $58450
So, the value of the bulldozer after 16 years is $58450.
A) To express the value of the bulldozer, V, as a function of how many years old it is, t, we need to consider the linear depreciation over its useful life of 25 years.
Linear depreciation means that the decrease in value is constant per year. In this case, the initial value of the bulldozer is $140,050, and its salvage value at the end of 25 years is $12,550.
Since depreciation is linear, we can calculate the decrease in value per year by finding the difference between the initial value and the salvage value, and then dividing it by the useful life of 25 years.
The decrease in value per year is given by:
Depreciation per year = (Initial value - Salvage value) / Useful life
Depreciation per year = ($140,050 - $12,550) / 25
Depreciation per year = $127,500 / 25
Depreciation per year = $5,100
Now, to express the value of the bulldozer, V, as a function of how many years old it is, t, we subtract the depreciation per year multiplied by the number of years from the initial value:
V(t) = Initial value - Depreciation per year * t
V(t) = $140,050 - $5,100 * t
B) To find the value of the bulldozer after 16 years, we substitute t = 16 into the function we derived in part A:
V(16) = $140,050 - $5,100 * 16
V(16) = $140,050 - $81,600
V(16) = $58,450
Therefore, the value of the bulldozer after 16 years is $58,450.