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) \(a \approx 2.6352 , b \approx 0.4756\)

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Definitions:

Demand Curve

A graphical representation that shows the relationship between the price of a product and the quantity of the product that consumers are willing and able to purchase at various prices.

Sensitive

Pertaining to something that requires careful handling due to its potential to cause a reaction or damage under certain conditions.

Ten-Year Period

A duration of ten years used as a measurement of time for planning, analysis, or investment purposes.

Price Elasticity

A measure of how the quantity demanded of a good is affected by a change in its price.