Find a Power Function That Models the Data in the Table

question 247

Multiple Choice

Find a power function that models the data in the table. Round to three decimal places if necessary.
- $$\begin{array} { c | c c c c c } \mathrm { x } & 1 & 2 & 3 & 4 & 5 \\\hline \mathrm { y } & 4 & 14 & 39 & 60 & 120\end{array}$$

• A) \(y = 2.085 x ^ { 3.734 }\)
• B) \(y = 27.8 x - 36\)
• C) \(\mathrm { y } = 2.309 \mathrm { x } ^ { 2.284 }\)
• D) \(y = 3.734 x ^ { 2.085 }\)

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Definitions:

MTBF

Mean Time Between Failures, a reliability metric for products and systems that estimates the average time between operational failures.

System Reliability

The probability of a system or component performing its required functions under stated conditions for a specified period of time.

Parallel Components

Components that are designed to work alongside each other within a system, often to increase redundancy and reliability.

Cost Curves

Graphical representations that show how the cost of producing a good or service changes with changes in the production volume.