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Express Lane Plus
Posts: 485
Rep: 2 0
4 weeks ago
2. The following table shows the 2002 private-party resale value of a 2000 Jeep Grand Cherokee Laredo in excellent condition as a function of the mileage.

Mileage (1000s of miles)
Resale value (dollars)
20
18,520
40
17,120
60
14,670
80
13,295
100
12,745
120
12,270

a) Why is a quadratic model a good fit for the data?
b) Would another model be a good choice for the data? Why or why not?
c) Find a quadratic model for the data.
d) Use your model to estimate the resale value for this Jeep at 52,000 miles.
e) Does your model have any limitations? (Base your answer on a plot of the data and the model.)
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Educator
4 weeks ago
For this, I had no choice but to use excel.

(a) The data fits the shape of a parabola when graphed. Eventually, the more miles you drive, the car will reach its minimum value, and that's what happens with quadratics, that is, they have either 1 maximum or 1 minimum.

(b) You may also use exponential decay model, because that too eventually reaches a minimum, but never quite reaches 0 (albeit, depends on the limits).

(c) Using excel: y = 5E-07x2 - 0.1418x + 21383, which means: \(y=0.0000005x^2-0.1418x+21383\)

(d) x @ 52,000 >\($15361.40\)

(e) Limitations is that restrictions haven't been set. Technically, you could place a negative x value and it'll output a negative mileage. Furthermore, it doesn't take into account that as miles increase, classic cars or vintage cars actually rise in value.
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