Question 1109262: A new truck costs $32,000. The truck’s value will depreciate over time, which means it will lose value. For tax purposes, depreciation is usually calculated linearly. If the truck is worth $24,500 after three years, write an explicit formula for the value of the truck after n years.
Answer by addingup(3677)   (Show Source):
You can put this solution on YOUR website! Formula:
V(t) = mt + b
Notice that this equation is in slope-intercept form, and is equivalent to
the slope-intercept formula you probably know: y = mx + b
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For your problem, let's find the slope of the line, how quickly the line drops year on year. This will be our annual depreciation cost.
We are given two points along the line, the beginning (0, 32,000) and the end (5, 10,300). Solve as in solving the slope-intercept:
m = [V(3)-V(0)]/3-0 = (24,500-32,000)/3-0 = -2,500
So, our slope m = -2,500
Note that the result is negative because the slope of the line is negative, the value of the truck goes down by 2,500 each year (depreciation).
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To find the value of the truck after 3 years, go to the original formula and substitute with the numbers you now know:
V(t) = mt + b
V(3) = -2,500(3) + 32,000
V(3 = -7,500 + 32,000
V(3) = 24,500 this is the value of the truck after 3 years
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Happy learning,
John
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