Solve.
-The data in the table show the number of burglaries reported in a small town for several years on record. $$\begin{array} { c | c }
\text { Year } & \text { \# of Burglaries } \
\hline 0 & 8 \
2 & 5 \
4 & 6 \
6 & 3 \
7 & 3 \
8 & 2 \
11 & 2 \
13 & 3 \
15 & 3
\end{array}$$ Determine the linear, quadratic, cubic, or quartic function that best fits the data.
A) $f ( x ) = 0.001 x ^ { 3 } + 0.03 x ^ { 2 } - 0.93 x + 7.78$
B) $f ( x ) = - 0.0003 x ^ { 4 } + 0.01 x ^ { 3 } - 0.07 x ^ { 2 } - 0.65 x + 7.68$
C) $f ( x ) = - 0.31 x + 6.15$
D) $f ( x ) = 0.0003 x ^ { 3 } + 0.01 x ^ { 2 } - 0.07 x + 7.68$

Question

Solve.
-The data in the table show the number of burglaries reported in a small town for several years on record. $$\begin{array} { c | c } 
\text { Year } & \text { \# of Burglaries } \
\hline 0 & 8 \
2 & 5 \
4 & 6 \
6 & 3 \
7 & 3 \
8 & 2 \
11 & 2 \
13 & 3 \
15 & 3
\end{array}$$ Determine the linear, quadratic, cubic, or quartic function that best fits the data. 
A) $f ( x ) = 0.001 x ^ { 3 } + 0.03 x ^ { 2 } - 0.93 x + 7.78$
B) $f ( x ) = - 0.0003 x ^ { 4 } + 0.01 x ^ { 3 } - 0.07 x ^ { 2 } - 0.65 x + 7.68$
C) $f ( x ) = - 0.31 x + 6.15$
D) $f ( x ) = 0.0003 x ^ { 3 } + 0.01 x ^ { 2 } - 0.07 x + 7.68$

Quizplus · Accepted Answer

Given the fluctuating nature of the data points, a quartic function (degree 4 polynomial) is more likely to accurately model the data because it can accommodate multiple turns in the graph, reflecting increases and decreases in the number of burglaries over time. Option B is a quartic function, which typically provides a better fit for data with multiple peaks and troughs compared to linear, quadratic, or cubic functions.

Solve -The Data in the Table Show the Number of Burglaries

Solve
-The Data in the Table Show the Number of Burglaries