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Question 124751: I need help with this word problem.
After 8 months of use, the value of Kathy's computer had depreciated to $890. After 10 months, the value had gone down to $750. Assume that the value of the computer, V, is a linear function of the number of months of use, t.
a) Write an equation for the value of the computer after t months of use.
b) How much did the computer cost originally?
c) What was the monthly depreciation?
Found 2 solutions by stanbon, Earlsdon:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! After 8 months of use, the value of Kathy's computer had depreciated to $890. After 10 months, the value had gone down to $750. Assume that the value of the computer, V, is a linear function of the number of months of use, t.
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You have two points:
(8,890) and (10,750)
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a) Write an equation for the value of the computer after t months of use.
Slope = (750-890)/(10-8) = -140/2 = -70
Form is V=mt+b ; you have V, m, t, and can solve for "b".
750 = -70*10 + b
b = 1450
EQUATION:
V(t)=-70t + 1450
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b) How much did the computer cost originally?
V(0) = -70*0+1450 = 1450
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c) What was the monthly depreciation?
$70
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Cheers,
Stan H.
Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website! The present value (V) of the computer is equal to the original cost (C) less the depreciation (D).
So you can start by writing:
But, you are to assume that the depreciation (D) is a linear function of (directly proportional to) the number of months of use (t). So the depreciation (D) can be expressed as:
 where k is the constant of proportionality. You can find the value of k as follows:
First, rewrite the equation for the value V in terms of the months of use, t, by replacing D with kt, as:
a)  You can write two equations, one for each of the given depreciation values and months of use.
Now substitute the given values of  ,  ,  , and  to get the two equations:
1)  Rewrite this as:
2)  Rewrite this as:
Now set these two equations equal to each other to get:
 Simplify and solve for k. Subtract 750 from both sides.
 Subtract 8*k from both sides.
 Divide both sides by 2.
b) Now you can find the original cost of the computer.
Substitute k = 70.
 or...
The original cost of the computer is $1,450.00
The monthly depreciation is just the value, k, or $70.00 per month.
Or you can calculate it as:
 = or...
 =
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