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Question 1087082: The depreciated value V of a machine is a linear function of time t in years. A machine that is purchased for $100000 today will be worth approximately $67681 in 3 years. Write the linear function V(t) that represents the value of the machine at a given time t.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! The value today is V = 100000 dollars when the time is t = 0, which is the starting time value.
The value in 3 years, when t = 3, is V = 67681 dollars
So we have two ordered pairs (0,100000) and (3,67681). I'm going to treat t as x, and treat V as y. So each ordered pair goes from the form (t,V) to (x,y). Using the (x,y) form we can use the slope formula
First point = (x1,y1) = (0,100000)
Second point = (x2,y2) = (3,67681)
So the slope is meaning that each year the value drops by $10,773
The y intercept is  because this is the starting value (at t = 0)
So we go from  to 
The last thing to do is replace x with t and replace y with V(t) to get 
Therefore the value function is
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Let's check the function. Plug t = 0 into the function to get
So that matches with the fact the initial value is $100,000
Now plug in t = 3
Which matches with the value after 3 years. So the answer is confirmed
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