Solve the Problem Above Is the Graph Of $45.05 \sin x$

Multiple Choice

Solve the problem.
-The data below represent the average monthly cost of natural gas in an Oregon home. $$\begin{array}{l}\begin{array} { l | c c c c c c } \text { Month } & \text { Aug } & \text { Sep } & \text { Oct } & \text { Nov } & \text { Dec } & \text { Jan } \\\hline \text { Cost } & 21.20 & 28.24 & 44.73 & 67.25 & 89.77 & 106.26\end{array}\\\\\begin{array} { l | c c c c c c } \text { Month } & \text { Feb } & \text { Mar } & \text { Apr } & \text { May } & \text { Jun } & \text { Jul } \\\hline \text { Cost } & 111.30 & 106.26 & 89.77 & 67.25 & 43.73 & 28.24\end{array}\end{array}$$


Above is the graph of $45.05 \sin x$ superimposed over a scatter diagram of the data. Find the sinusoidal function o form $y = A \sin ( \omega x - \varphi ) + B$ which best fits the data.

A) $y = 45.05 \sin \left( \frac { \pi } { 8 } t + 12 \right) + 21.20$
B) $y = 45.05 \sin \left( \frac { \pi } { 4 } x - \frac { 2 \pi } { 3 } \right) + 21.20$
C) $y = 45.05 \sin \left( \frac { \pi } { 6 } x - \frac { 2 \pi } { 3 } \right) + 66.25$
D) $y = 45.05 \sin \left( \frac { \pi } { 6 } x - \frac { \pi } { 12 } \right) + 66.25$