1 2 3 obtain and plot the first through fourth degree polynomials for

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Question

1.
2.
3.
Obtain and plot the first-through fourth-degree polynomials for the following data: x = 0,
1, 2, 3, 4, and 5, and y = 0, 1, 60, 40, 41, and 47. Find the coefficients and the J values,
and write down the first- through fourth-degree polynomial equations derived from the
modeling. (20 pts.)
The population data for a certain country are as follows:
Year
2004 2005 2006 2007 2008 2009
Population (million) 10 10.9 11.7 12.6 13.8 14.9
Obtain a function that describes these data. Plot the function and the data on the same
plot. Estimate when the population will be double its 2004 size. (40 pts.)
The following data give the drying time T of a certain paint as a function of the amount of
a certain additive A.
A (oz.)
T (min)
0 1 2 3
130 115 110 90
45
89 89
95
6 7 8
100 110
9
125
a.
Find the first-, second-, third-, and fourth-degree polynomials that fit the data, and
plot each polynomial with the data. Determine the quality of the curve fit for each by
computing J, S, and r². (20 pt.)
b. Use the polynomial giving the best fit to estimate the amount of additive that
minimizes the drying time. (20 pts.)