The table below gives the number of births, in thousands, to females over the age of 35 for a particular state every two years from 1994 to 2010. $$\begin{array} { c | c }
& \text { Births } \
\text { Year } & \text { (thousands) } \
\hline 1994 & 42.5 \
\hline 1996 & 29.9 \
\hline 1998 & 36.0 \
\hline 2000 & 56.9 \
\hline 2002 & 71.1 \
\hline 2004 & 69.9 \
\hline 2006 & 57.2 \
\hline 2008 & 37.1 \
\hline 2010 & 25.9
\end{array}$$ Use technology to find the quartic function that is the best fit for this data, where x is the number of years after 1994.
According to the model, when will the number of births to females over the age of 35 first reach 80,000?
A) 2015
B) 2014
C) 2016
D) 2013

Question

The table below gives the number of births, in thousands, to females over the age of 35 for a particular state every two years from 1994 to 2010. $$\begin{array} { c | c } 
& \text { Births } \
\text { Year } & \text { (thousands) } \
\hline 1994 & 42.5 \
\hline 1996 & 29.9 \
\hline 1998 & 36.0 \
\hline 2000 & 56.9 \
\hline 2002 & 71.1 \
\hline 2004 & 69.9 \
\hline 2006 & 57.2 \
\hline 2008 & 37.1 \
\hline 2010 & 25.9
\end{array}$$ Use technology to find the quartic function that is the best fit for this data, where x is the number of years after 1994.
According to the model, when will the number of births to females over the age of 35 first reach 80,000?
A) 2015
B) 2014
C) 2016
D) 2013

Quizplus · Accepted Answer

Using technology to fit a quartic function to the given data, the function that best fits the data can be found. By setting the function equal to 80 (since the data is in thousands, 80,000 births correspond to 80 in the function) and solving for x, where x is the number of years after 1994, we can find when the number of births first reaches 80,000. The correct year, according to the model, is 2013.

The Table Below Gives the Number of Births, in Thousands