Question 1097601: A manufacturer buys a new machine costing $130,000. It is estimated that the machine has a useful lifetime of fifteen years and a salvage value of $4000 at that time.
(a) Find a formula for the value of the machine after t years, where 0 ≤ t ≤ 15.
V(t) =
(b) Find the value of the machine after ten years.
$
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i believe it works like this.
the value today is 130,000
the value in 15 years is 4000.
with straigh line depreciation, the decrease in value each year is calculated using the formula:
y = mx + b.
m is the slope and b is the y-intercept.
the y-intercept is the value of y when x = 0.
that would be 130,000 which is the value of the machine when it is bought.
therefore the equation becomes:
y = mx + 130,000.
the formula for the slope is m = (y2 - y1) / (x2 - x1)
(x1,y1) is equal to 0, 130,000)
(x2,y2) is equal to (15, 4,000)
m becomes equal to (4,000 - 130,000) / (15 - 0) = -136,000 / 15 = -8400.
formula becomes y = -8400 * x + 130,000
when x = 0, y = 130,000
when x = 15, y = 4,000.
a graph of that equation is shown below showing the value of the machine after 10 years.
that value is 46000 because y = -8400 * x + 130,000 becomes y = -8400 * 10 + 130,000 when x = 10 which becomes y = -84000 + 130,000 which becomes y = 46,000.
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