Find a Power Function That Models the Data in the Table

question 155

Multiple Choice

Find a power function that models the data in the table. Round to three decimal places if necessary.
- $\begin{array}{c|ccccc}x & 2 & 4 & 6 & 8 & 10 \\\hline y & 6.7 & 12.1 & 15.4 & 18.8 & 22.7\end{array}$

• A) \(y = 1.935 x + 3.53\)
• B) \(y = 0.742 x ^ { 4.104 }\)
• C) \(y = 5.887 x ^ { 1.155 }\)
• D) \(y = 4.104 x ^ { 0.742 }\)

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Definitions:

Marginal Cost (MC)

Marginal Cost, abbreviated as MC, refers to the increase in total production cost that arises from producing an additional unit of output, emphasizing the concept of optimizing production levels.

Average Total Cost (ATC)

The total cost divided by the quantity of output produced, representing the per-unit cost of production.

Marginal Revenue (MR)

The additional financial gain a firm secures by selling one more unit of its product or service.

Purely Competitive

A market structure characterized by a large number of small firms, a homogeneous product, free entry and exit, and complete information, leading to price taking behavior.