A company paid $150,000 for a new 18-wheeler. When it is 9 years old it will be worth $42,000. Using straight-line depreciation, the value of the truck in dollars, V, is a linear function of its age in years, n. Find the function and the value when the truck is 4 years old.
V = Vo - Vo*r*T = $42,000.
150,000 - 150,000*r*9 = 42,000.
1 - 9r = 0.28,
9r = 0.72,
r = 0.08/yr. = Annual depreciation rate.
V = Vo - Vo*r*T.
V = 150,000 - 150,000*0.08*4 = $102,000.
Well, let's calculate the annual depreciation of the truck first. To do that, we subtract the final value from the initial value and divide it by the number of years:
Depreciation per year = (Initial value - Final value) / Number of years
Depreciation per year = ($150,000 - $42,000) / 9
Depreciation per year ≈ $11,111.11
Now, using straight-line depreciation, we can find the value of the truck at any given year using the formula:
V = Initial value - (Depreciation per year * Number of years)
Therefore, the function is:
V(n) = $150,000 - ($11,111.11 * n)
Now, to find the value of the truck when it is 4 years old, we substitute n = 4 into the function:
V(4) = $150,000 - ($11,111.11 * 4)
V(4) = $150,000 - $44,444.44
V(4) ≈ $105,555.56
So, when the truck is 4 years old, its value will be approximately $105,555.56. Hope that puts a smile on your face!
To find the linear function representing the value of the truck, we need to calculate the depreciation per year.
The difference in value between the purchase price and the estimated worth after 9 years is $150,000 - $42,000 = $108,000.
The depreciation per year is then $108,000 / 9 years = $12,000/year.
Therefore, the linear function representing the value of the truck is: V(n) = 150,000 - 12,000n, where n is the age of the truck in years.
To find the value of the truck when it is 4 years old (n = 4), plug in the value of n into the function:
V(4) = 150,000 - 12,000 * 4
V(4) = 150,000 - 48,000
V(4) = $102,000
Therefore, when the truck is 4 years old, its value will be $102,000.
To find the linear function that represents the value of the truck in dollars, we need to determine the rate at which the value decreases per year.
First, let's calculate the depreciation per year. The truck loses $150,000 - $42,000 = $108,000 over 9 years.
Therefore, the depreciation per year is $108,000 / 9 = $12,000.
Now, let's find the value of the truck when it is 4 years old. We'll subtract 4 years of depreciation from the initial value of $150,000:
$150,000 - ($12,000 * 4) = $150,000 - $48,000 = $102,000.
So, the linear function that represents the value of the truck in dollars, V, is given by:
V(n) = $150,000 - ($12,000 * n)
Where n is the age of the truck in years.
To find the value of the truck when it is 4 years old, substitute n = 4 into the function:
V(4) = $150,000 - ($12,000 * 4) = $150,000 - $48,000 = $102,000.
Therefore, when the truck is 4 years old, its value will be $102,000.
Look at it as being given two ordered pairs , (0,150000) and (9,42000)
slope = (42000-150000)/(9-0) = -108000/9 = -12000
so value = V(n) = -12000n + b
but (0,150000) is the "y-intercept"
your function is
V(n) = -12000n + 150000
for the 2nd part, plug in n = 4