Find a Power Function That Models the Data in the Table

question 7

Multiple Choice

Find a power function that models the data in the table. Round to three decimal places if necessary.
-The percent of people who say they plan to stay in the same job position until they retire has decreased over recent years, as shown in the table below. $$\begin{array} { c | c c c c c c } \text { Year } & 2005 & 2006 & 2007 & 2008 & 2009 & 2010 \\\hline \text { Percent } & 42 & 38 & 35 & 34 & 30 & 26\end{array}$$ Find a power function that models the data in the table using an input equal to the number of years from 2000.
According to the unrounded model, in what year will only 23% of people plan to stay in the same job position until
Retirement?

• A) 2011
• B) 2015
• C) 2013
• D) 2016

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Definitions:

Autoregressive Model

A model for forecasting a time series that uses the relationship between an observation and a number of lagged observations.

Time Series Data

Data points collected or recorded at regular time intervals, used for analyzing trends, cycles, and seasonal variations over time.

Consecutive Residuals

The differences between observed and predicted values in a sequence, following each other without interruption.

Seasonal Variation

Patterns or fluctuations in data or activities that recur with consistent regularity in specific seasons or times of the year.