Modeling Data The table shows the net sales x (in billions of dollars), the total assets y (in billions of dollars), and the share holder's equity - (in billions of dollars) for Walmart for the years 2010 through 2015. (Source: Wal-Mart Stares, Inc.)
Year |
2010 |
2011 |
2012 |
2013 |
2014 |
2015 |
x |
405.0 |
418.5 |
443.4 |
465.6 |
473.1 |
482.2 |
y |
170.7 |
180.8 |
193.4 |
203.1 |
204.8 |
203.7 |
z |
70.7 |
68.5 |
71.3 |
76.3 |
76.3 |
81.4 |
A model for the data is
(a) Complete a fourth row in the table using the model to approximate ? for the given values of x and y. Compare the approximations with the actual values of x.
(b) Which of the two variables in this model has more influence on share holder's equity? Explain.
(c) Simplify the expression for f(x, 150) and interpret its meaning in the context of the problem.
Complete the fourth row in the provided table using the model, to approximate z for the provided values of x & y. Compare the approximation with the actual value of Z.
Given:
Modeling data shown in below table:
The table shows the net sales x in billions of dollars.
Total assets in billions of dollars.
Shareholder Equity z in billions of dollars
A model for data is given as
a)
Year | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 |
450 | 418.5 | 443.4 | 465.6 | 473.1 | 482.2 | |
170.7 | 180.8 | 193.4 | 203.1 | 204.8 | 203.7 | |
70.7 | 68.5 | 71.3 | 76.3 | 76.3 | 81.4 | |
Approximate z using model | 70.04 | 69.23 | 71.66 | 74.82 | 76.92 | 81.54 |
Zmodel-Zgiven | -0.6551 | 0.73 | 0.36 | -1.47 | 0.62 | 0.14 |
b) Total assets represented by ‘y’ have more influence on the value of ‘z’ which represents the shareholder’s equity.
c)
a)
The provide model is
Similarly for other years,
Put the values of & y, to approximate the values of z.
Compare approximations with actual values of z, to get values shown in below table.
Year | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 |
450 | 418.5 | 443.4 | 465.6 | 473.1 | 482.2 | |
170.7 | 180.8 | 193.4 | 203.1 | 204.8 | 203.7 | |
70.7 | 68.5 | 71.3 | 76 |
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