Solve.
-The data in the table show the number of burglaries reported in a small town for several years on record. $$\begin{array} { c | c }
\text { Year } & \text { \# of Burglaries } \
\hline 0 & 4 \
2 & 3 \
4 & 2 \
6 & 2 \
7 & 2 \
8 & 3 \
11 & 4 \
13 & 6 \
15 & 8
\end{array}$$ Determine the linear, quadratic, cubic, or quartic function that best fits the data.
A) $f ( x ) = 0.28 x + 1.7$
B) $f ( x ) = - 0.0007 x ^ { 3 } + 0.086 x ^ { 2 } - 0.79 x + 4.07$
C) $f ( x ) = - 0.00004 x ^ { 4 } + 0.0006 x ^ { 3 } + 0.07 x ^ { 2 } - 0.76 x + 4.05$
D) $f ( x ) = 0.07 x ^ { 2 } - 0.71 x + 3.99$

Question

Solve.
-The data in the table show the number of burglaries reported in a small town for several years on record. $$\begin{array} { c | c } 
\text { Year } & \text { \# of Burglaries } \
\hline 0 & 4 \
2 & 3 \
4 & 2 \
6 & 2 \
7 & 2 \
8 & 3 \
11 & 4 \
13 & 6 \
15 & 8
\end{array}$$ Determine the linear, quadratic, cubic, or quartic function that best fits the data. 
A) $f ( x ) = 0.28 x + 1.7$
B) $f ( x ) = - 0.0007 x ^ { 3 } + 0.086 x ^ { 2 } - 0.79 x + 4.07$
C) $f ( x ) = - 0.00004 x ^ { 4 } + 0.0006 x ^ { 3 } + 0.07 x ^ { 2 } - 0.76 x + 4.05$
D) $f ( x ) = 0.07 x ^ { 2 } - 0.71 x + 3.99$

Quizplus · Accepted Answer

The quartic function (option C) is likely the best fit because it allows for more flexibility in fitting the data, which shows a non-linear trend with varying rates of increase and decrease in the number of burglaries over the years. Linear, quadratic, and cubic functions may not capture the complexity of the data's pattern as effectively as a quartic function.

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

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