A study was conducted to investigate the relationship between the resale price, y (in hundreds of dollars), and the age, x (in years), of midsize luxury American automobiles. The equation of the line of best fit was determined below.
y = 179.3 − 20.78x
(a) Find the resale value in dollars of such a car when it is 3 years old.
$
(b) Find the resale value in dollars of such a car when it is 6 years old.
$
(c) What is the average annual decrease in the resale price in dollars of these cars?
To find the resale value of the car at a specific age, we can substitute the given age value into the equation of the line of best fit.
(a) To find the resale value when the car is 3 years old, we substitute x = 3 into the equation:
y = 179.3 - 20.78(3)
y = 179.3 - 62.34
y ≈ 116.96
Therefore, the resale value of the car when it is 3 years old is approximately $116.96.
(b) To find the resale value when the car is 6 years old, we substitute x = 6 into the equation:
y = 179.3 - 20.78(6)
y = 179.3 - 124.68
y ≈ 54.62
Therefore, the resale value of the car when it is 6 years old is approximately $54.62.
(c) To find the average annual decrease in the resale price of the cars, we can look at the slope of the equation. In this case, the coefficient of x, -20.78, represents the decrease in resale price per year.
Therefore, the average annual decrease in the resale price of these cars is $20.78.