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) \(y = 27.35 \sin \left( \frac { \pi } { 6 } x - \frac { 2 \pi } { 3 } \right) + 55.25\)

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Definitions:

Elasticity Of Demand

A measure of how much the quantity demanded of a good changes in response to a change in its price.

Mark-Up

A percentage added to the cost price to determine the selling price.

Elasticity Of Demand

This metric indicates the reaction of the quantity of a product demanded by consumers to shifts in its price, expressed as the ratio of the percentage change in demand to the percentage change in the product's price.

Marginal Costs

The cost associated with producing one additional unit of a good, highlighting the changes in total production cost.