Find a Power Function That Models the Data in the Table

question 10

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. $\begin{array} { l c } \underline { \text { Year } } & \text { New Cases (thousands) } \\ 2005 & 3.0 \\ 2006 & 3.4 \\ 2007 & 4.6 \\ 2008 & 5.4 \\ 2009 & 6.0 \\ 2010 & 16.1 \end{array}$
Let $x = 1$ correspond to 2005 and let $y$ 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) \(y = 6.69 x ^ { 2 } - 3.645 x + 0.823\)
• B) \(y = 0.823 x ^ { 2 } - 3.645 x + 6.69\)
• C) \(y = 0.945 x ^ { 2 } - 5.212 x + 8.921\)
• D) \(y = 0.623 x ^ { 2 } - 5.645 x + 8.69\)

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