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:

Double-Blind Study

A research method in which both the subjects and the researchers are unaware of which group (test or control) the subjects belong to, to prevent bias.

Experimental

Pertaining to a methodical procedure carried out with the goal of verifying, falsifying, or establishing the validity of a hypothesis.

Control Groups

Groups in an experiment that do not receive the treatment being tested, enabling comparison to groups that do receive the treatment to assess its effect.

Investigator

An individual, often a scientist or researcher, who conducts detailed and systematic examination or inquiry into something through research and experimentation.