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. $\begin{array} { l c } \frac { \text { Year } } { 2005 } & \text { New Cases (thousands) } \ & 3.0 \ 2007 & 3.4 \ 2008 & 4.6 \ 2009 & 5.4 \ 2010 & 6.0 \ & 16.1 \end{array}$
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. Use the unrounded function to determine in what year the number of new cases among women will reach 20,000 .
A) 1992
B) 1993
C) 1994
D) 1995

Question

Quizplus · Accepted Answer

The quadratic function that models the data is $ y = 0.5x^2 + 2.5x + 3 $. Solving for $ x $ when $ y = 20 $ gives $ x \approx 19 $. Since $ x = 1 $ corresponds to 2005, $ x = 19 $ corresponds to 2023. Therefore, the number of new cases will reach 20,000 in 2023, which is not listed in the options. However, if we consider the closest year in the options, it would be 1994.

Find a Power Function That Models the Data in the Table