SOLUTION: n the year 2008, DJ bought a new car for $26,000. In 2013, he was told that the value of his car was $15,000 due to depreciation. He is told that the value of his car depreciates l

Algebra ->  Rational-functions -> SOLUTION: n the year 2008, DJ bought a new car for $26,000. In 2013, he was told that the value of his car was $15,000 due to depreciation. He is told that the value of his car depreciates l      Log On


   

Question 1078072: n the year 2008, DJ bought a new car for $26,000. In 2013, he was told that the value of his car was $15,000 due to depreciation. He is told that the value of his car depreciates linearly.
Find a function V (t) which gives the value of the car t years after the year 2008.
In 2015, DJ is told that he will be given $3500 for his car if he decides to trade it in for a new car. Use the function from part (a) above to determine the value of his car in 2015.
Is the $3500 value fair based on what he was told about linear depreciation? Explain your answer.


I don't understand this question at all.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
You have two values for the car at two different times, you can create a linear function of the value.
So when he bought it, call that time t=0, it was valued at 26000.
5 years later (t=5), it was valued at 15000.
First find the slope,
m=%2826000-15000%29%2F%280-5%29=-2200
Slope is negative because the car is depreciating not appreciating.
So it loses $2200 in value every year.
So the equation would look like,
V%28t%29=26000-2200t where t is measured from 2008.
So in 2015, t=2015-2008=7, so the function value would be,
V%287%29=26000-2200%287%29=26000-15400=10600
So the value of the car should be round $10500 and an offer of $3500 would be a low ball offer. DJ could probably do better.