SOLUTION: The depreciated value VV 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 33 years. Write t
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Question 1087074: The depreciated value VV 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 33 years. Write the linear function V(t) that represents the value of the machine at a given time t.
My work---> 100,1000---->67,681 3yrs
67,681v+3=100,000 this is what I got but I'm not sure.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I think you meant to say "The depreciated value V" instead of "The depreciated value VV". I changed the VV to V.
The value today is V = 100000 dollars when the time is t = 0, which is the starting time value.
The value in 33 years, when t = 33, is V = 67681 dollars
So we have two ordered pairs (0,100000) and (33,67681). 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) = (33,67681)
Use a calculator here. The decimal form is approximate (the '36' portion repeats forever)
So the slope is roughly
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
-------------------------------------------------
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 = 33
Which matches with the value after 33 years. So the answer is confirmed
Side Note: if you use the fraction form for the slope then you won't run into rounding errors. The fact that we're rounding to 2 decimal places means that we don't have to worry about precision too much as long as the slope is expressed to 3 decimal places or more. You're probably wondering what the slope means? If so, then the slope is simply the rate of value decay or drop. In this case, the slope -979.3636 means the value V(t) is decreasing by $979.36 each year. The actual drop is a bit more than that but you can only round to the nearest hundredth for money problems like this.
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