SOLUTION: This question is along the lines of determining whether a data set is linear, quadratic, or exponential. The data set is this: (the depreciation of a used car over time) X = Year

Question 1122467: This question is along the lines of determining whether a data set is linear, quadratic, or exponential.
The data set is this: (the depreciation of a used car over time)
X = Years
Y = Value in dollars
(0, 12,575)
(1, 11,065)
(2, 9,750)
(3, 8,520)
(4, 7,540)
To me, this data set does not seem to linear, quadratic, or exponential, however my textbook does not say anything about a 'neither' or 'none' option. My only guess is it might be exponential?
Found 2 solutions by josgarithmetic, solver91311:
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
Plot the points. How does that plot appear? "Depreciation"? This would be a decrease trend. Your points suggest such a trend without any doubt.
.
The plot looks nearly linear but looks like a curve, concave up, still decrease from left to right. You could try testing for quadratic model, but the plot appears nearly a line.

(Put your points, without the place-value comma separators, into http://www.shodor.org/interactivate/activities/OrderedSimplePlot/ ).
.

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Putting the data into a graphing calculator and running a regression analysis gives a Coefficient of Determination for a Linear curve of best fit of 0.9941 which is pretty good, but both the 2nd-degree polynomial fit and the exponential fit is 0.9999. The difference is that the quadratic reaches a minimum somewhere out around year 9 or 10 whereas the exponential continues to decrease, i.e. it is asymptotic to the x-axis.

So what you have to decide is whether you have a classic used car that at some point will start to appreciate in value, or do you have the standard piece of junk that will someday be nearly worthless. Your call, but you can argue either answer.

John

My calculator said it, I believe it, that settles it

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