The table below gives the violent crime rate (per 100,000 people) for a particular state every five years from 1970 to 2010.
$\begin{array} { c | c }
\text { Year } & \text { Rate } \
\hline 1970 & 4.8 \
\hline 1975 & 5.0 \
\hline 1980 & 5.9 \
\hline 1985 & 7.3 \
\hline 1990 & 8.9 \
\hline 1995 & 10.4 \
\hline 2000 & 11.6 \
\hline 2005 & 12.3 \
\hline 2010 & 12.1
\end{array}$
Use technology to find the cubic function that is the best fit for this data, where x is the number of years after 1970. Use the model to estimate the violent crime rate for the year 2014.
A) 11.6
B) 11.4
C) 11.8
D) 11

Question

The table below gives the violent crime rate (per 100,000 people) for a particular state every five years from 1970 to 2010. 
$\begin{array} { c | c } 
\text { Year } & \text { Rate } \
\hline 1970 & 4.8 \
\hline 1975 & 5.0 \
\hline 1980 & 5.9 \
\hline 1985 & 7.3 \
\hline 1990 & 8.9 \
\hline 1995 & 10.4 \
\hline 2000 & 11.6 \
\hline 2005 & 12.3 \
\hline 2010 & 12.1
\end{array}$ 
Use technology to find the cubic function that is the best fit for this data, where x is the number of years after 1970. Use the model to estimate the violent crime rate for the year 2014.
A) 11.6
B) 11.4
C) 11.8
D) 11

Quizplus · Accepted Answer

Using technology (such as a graphing calculator or software that can perform regression analysis), you can input the given data points and perform a cubic regression to find the best-fit cubic function. Applying this function with $x = 44$ (since 2014 is 44 years after 1970) will give an estimated violent crime rate. The exact value might slightly vary depending on the regression tool used, but it should be close to the choice provided.

The Table Below Gives the Violent Crime Rate (Per 100,000