Question 1099057: Dog Years. A dog's life span is typically much shorter than that of a human. Age equivalents for dogs and humans are listed in the table below.
Age of Dog, x (in years)
0.25
0.5
1
2
4
6
8
10
14
18
21
Human Age, h (x) (in years)
5
10
15
24
32
40
48
56
72
91
106
a) Use a graphing calculator to fit linear and cubic functions to the data. Which function has the better fit?
b) Using the function from part (a), estimate the equivalent human age for dogs that are 5, 10, and 15 years old.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Linear is y=4.55x+10.31 r^2 of 0.997
Cubic is y=0.103x^3-.34x^2+7.40x+6.62 and r^2 is 0.997
when x=5, y=48.0
x=10, y=112.62
x=15, y=388.745
cubics become very large as x increases modestly
linear had almost same fit
x=5
33.06
x=10
55.86
x=15
78.56
so while the R^2 is slightly better for the cubic function, the linear approximates everything much better.
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