Solve the Problem Find a Sinusoidal Function of the Form $y = A \sin ( \omega x - \varphi ) + B$

question 115

Multiple Choice

Solve the problem.
-A town's average monthly temperature data is represented in the table below: $$\begin{array} { l | c } { \text { Month, x } } & \begin{array} { c } \text { Average Monthl } \\\text { Temperature, }\end{array} \\\hline \text { January, } 1 & 27.9 \\\text { February, 2 } & 30.1 \\\text { March, } 3 & 39.8 \\\text { April, } 4 & 55.8 \\\text { May, 5 } & 70.4 \\\text { June, } 6 & 79.9 \\\text { July, } 7 & 82.6 \\\text { August, } 8 & 77.9 \\\text { September, } 9 & 77.9 \\\text { October, } 10 & 56.3 \\\text { November, } 11 & 43.4 \\\text { December, } 12 & 31.1\end{array}$$ Find a sinusoidal function of the form $y = A \sin ( \omega x - \varphi ) + B$ that fits the data.

• A) \(y = 82.6 \sin \left( \frac { \pi } { 6 } x - \frac { 2 \pi } { 3 } \right) + 27.9\)
• B) \(y = 27.9 \sin \left( \frac { \pi } { 6 } x - \frac { \pi } { 4 } \right) + 82.6\)
• C) \(y = 55.25 \sin \left( \frac { \pi } { 6 } x - \frac { \pi } { 4 } \right) + 27.35\)
• D) \(y = 27.35 \sin \left( \frac { \pi } { 6 } x - \frac { 2 \pi } { 3 } \right) + 55.25\)

---

Definitions:

Store of Value

An asset that can be saved, retrieved, and exchanged at a later time without significant loss of value.

Money

A medium of exchange, a unit of account, and a store of value, used to facilitate transactions.

Wealth

An abundance of valuable resources or valuable material possessions, often measured in terms of assets like money, real estate, and personal property.

Bank Holding Company

A corporation that owns banks.