SOLUTION: A company's assets have a value of $30,000 at the beginning of the year 1999. By the beginning og 2001 the assets has depreciated to $26,000. 1) Assuming that the depreciation is

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Question 164053: A company's assets have a value of $30,000 at the beginning of the year 1999. By the beginning og 2001 the assets has depreciated to $26,000.
1) Assuming that the depreciation is linear, write the linear equation rating the value V of the assest in terms of the years passed since the beginning of 1999.
2)Find the value of the asest in the year 2006
3)Find after how many years the value of the asset will be $7,000.
4)Find after how many years wil the asset be worthless(value=0)
Answer by MRperkins(300) About Me  (Show Source):
You can put this solution on YOUR website!
ok, the first thing we need is to find the formula:
The problem says that the formula is linear so let's use the slope-intercept form or y=mx+b where m=slope and b=the y-intercept.
Remember that the slope is simply how much y changes for each unit of x. So in this situation when x moves from 1999 to 2001 the y changes from 30,000 to 26,000.
Formula: slope=(change in y)/(change in x)
or
slope=%28y1-y2%29%2F%28x1-x2%29
or
slope=%2830000-26000%29%2F%281999-2001%29
slope=4000%2F-2
slope=-2000
So in this case x changed 2 and y changed -4,000, so to find out the change per year instead of per 2 years: divide -4000 by 2 and you get the change in y divided by the change in x or -2000
now we know that y=-2000x+b
the y-intercept or "b" is the y value when x=0 and x is the number of years passed since the beginning of 1999 so when x=0 y=30,000
therefore our formula is y=-2%2C000x%2B30%2C000
Part 2
Find the value of the asset in the year 2006:
2006-1999=7
so find the value of y when x=7
y=-2000(7)+30000
y=-14000+30000
y=16000
Part 3
Find after how many years the value of the asset will be $7,000.
let y=7000 and solve for x
7000=-2000x+30000
subtract 30000 from each side
-23000=-2000x
divide each side by -2000
11.5=x
so the value of assets will be $7000 after 11.5 years
Part 4
Find after how many years wil the asset be worthless(value=0)
let y=0 and solve for x
0=-2000x+30000
subtract 30000 from both sides
-30000=-2000x
divide each side by -2000
15=x
so the value of assets will be worthless after 15 years
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I hope this helps
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