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Find a Power Function That Models the Data in the Table

Question 229

Multiple Choice

Find a power function that models the data in the table. Round to three decimal places if necessary.
-The table shows the number of new cases of a certain disease among women in six consecutive years. Data are in thousands rounded to the nearest hundred.  Year  New Cases (thousands)  20053.020063.420074.620085.420096.0201016.1\begin{array} { l c } \underline { \text { Year } } & \text { New Cases (thousands) } \\ 2005 & 3.0 \\ 2006 & 3.4 \\ 2007 & 4.6 \\ 2008 & 5.4 \\ 2009 & 6.0 \\ 2010 & 16.1 \end{array}
Let x=1x = 1 correspond to 2005 and let yy be the number of new cases (in thousands) among women in year x. Find a quadratic function to model the data. Round to three decimal places if necessary.


A) y=6.69x23.645x+0.823y = 6.69 x ^ { 2 } - 3.645 x + 0.823
B) y=0.823x23.645x+6.69y = 0.823 x ^ { 2 } - 3.645 x + 6.69
C) y=0.945x25.212x+8.921y = 0.945 x ^ { 2 } - 5.212 x + 8.921
D) y=0.623x25.645x+8.69y = 0.623 x ^ { 2 } - 5.645 x + 8.69

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