Just like cell phones, most car values decrease over time. For example, in 2004,
ID: 3281977 • Letter: J
Question
Just like cell phones, most car values decrease over time. For example, in 2004, a new Toyota Prius sold for $20,300. In 2012, the Kelley Blue Book value for the same car was estimated to be $9,900. The 2004 Toyota Prius depreciated over time. Use this information to answer the following problems.
Assume the depreciation is linear. What is the rate of change of a linear model that represents the value of the Prius over time?
___dollars per year
Create a linear model of the value of the Prius, where V is the value, and t is the number of years after 2004. What input values make sense for t?
What is the vertical intercept of the graph of the model? (0, )
What does it represent in the context of this problem?
Use your model to estimate the value of the Prius in 2015.
$___
Explanation / Answer
T1= 2004 price = 20,300 and T2 = 2012 , price = 9900
m = rate of change = y2 - y1 / t2 - t1 = 9900 - 20,300 / 2012 - 2004 = -1300 dollars per year
y-y1 = m(t-t1)
y - 20300 = -1300(t-0)
=> y = 20300- 1300t
To make sense
20300- 1300t >= 0 => t <= 20300 / 1300 = 15.6
2004 <= t < = 2019.6
vertical interceopt => t = 0 , y = 20300
Vertical interecept is 20300 and it represents the starting price of car.
t = 2015 - 2004 = 11
y = 20300- 1300 * 11 = 6000
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