SOLUTION: The value of a certain car decreases at the rate of 300 dollars each month after being prucahsed new. Suppose that the car is worth $17,000 when it is 2 years old. A) Determin

Question 198308: The value of a certain car decreases at the rate of 300 dollars each month after being prucahsed new. Suppose that the car is worth $17,000 when it is 2 years old.
A) Determine a linear function that will give the value of the car as a function of months since being purchased.
B)Use this model to determine the value of the car after 4 years.
Answer by Madgamer107(9) (Show Source): You can put this solution on YOUR website!
Well, because you know that a linear function is required, it should resemble the form . In the case of this problem, y can represent the value of the car and x can represent the age of the car (in months). The problem also tells you that its decreasing at a rate of 300 dollars each month, so the slope, m, is -300; now we know that . It's also stated that the care is worth $17,000 when it is 2 years, or 24 months, old. So it is now possible to find the exact equation of the line by plugging in!
17000 = -300(24) + b
17000 = -7200 + b
24200 = b

Then, for part b, they ask for the price (y) after 4 years, or 48 months. Since you have a model now, you can just plug in and solve!
y = -300x + 24200
y = -300(48) + 24200
y = -14400 + 24200
y = 9,800
Therefore, according to the model, the price after 4 years will be $9,800. Hope I helped!
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