Find a Power Function That Models the Data in the Table

question 65

Multiple Choice

Find a power function that models the data in the table. Round to three decimal places if necessary.
-The table shows the population of a certain city in various different years. Use regression to find values for a and b so that f(x) = axb models this data, where x represents the number of years since 1990 and f(x) is the
Population of the city in hundreds of thousands. Round your answers to 4 decimal places. $\begin{array}{l|ccccc}\text { Year } & 1991 & 1995 & 1999 & 2003 & 2007 \\\hline \text { Population (hundreds of thousands) } & 3.2 & 4.1 & 5.7 & 9.6 & 14.1\end{array}$

• A) \(\mathrm { a } \approx 1.8506 , \mathrm {~b} \approx 0.5121\)
• B) \(a \approx 2.1375 , b \approx 0.4432\)
• C) \(\mathrm { a } \approx 1.7025 , \mathrm {~b} \approx 0.5375\)
• D) \(a \approx 2.6352 , b \approx 0.4756\)

Analyze the impact of changes in production levels on marginal cost.

Examine the relationship between marginal cost and average cost curves.

Understand the effects of changes in fixed costs on average total and variable costs.

Understand the distinction between different types of clinical assessment tools, including response inventories, projective tests, and personality inventories.

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