The tables below give Social Security Administration data for the U S average annual wage from 2011 and projected to 2021 and for selected years from 2012 and projected to 2050 (a) Make a scatter plot of each of these data sets with x as the number of years past 2010 (b) Decide which one function type could be used as a model for both data sets and find the two models Let a(x) be the model for the data to 2021 and A(x) be the one for data to 2050 Report both models with 4 significant digit coefficients (c) How well do the reported models agree for the data points for 2020 and for 2050 (d) When does each reported model predict the average annual wage will reach $150,000 Data to 2021 (in dollars) Data to 250 (in thousands of dollars) Year 2013 2011 2012 2014 Wage 44,644 48,595 43,009 46,496 Year 2017 2015 2016 2018 Wage 50,893 58,698 53,317 55,989 Year 2019 2020 2021 Wage 61,179 63,676 66,161 Year 2012 2014 2016 2018 Wage 44 6 48 6 53 3 58 7 Year 2020 2025 2030 2035 Wage 63 7 76 8 93 2 113 2 Year 2040 2045 2050 Wage 137 6 167 1 202 5

Question: The tables below give Social Security Administration data for the U.S. average annual wage from 2011 and projected to 2021 and for selected years from

The tables below give Social Security Administration data for the U.S. average annual wage from 2011 and projected to 2021 and for selected years from 2012 and projected to 2050.

(a) Make a scatter plot of each of these data sets with x as the number of years past 2010.

(b) Decide which one function type could be used as a model for both data sets and find the two models. Let a(x) be the model for the data to 2021 and A(x) be the one for data to 2050. Report both models with 4 significant digit coefficients.

(d) When does each reported model predict the average annual wage will reach $150,000?

Data to 2021 (in dollars)

Year 2013 2011 2012 2014 Wage 44,644 48,595 43,009 46,496 Year 2017 2015 2016 2018 Wage 50,893 58,698 53,317 55,989 Year

Data to 250 (in thousands of dollars)

Year 2012 2014 2016 2018 Wage 44.6 48.6 53.3 58.7 Year 2020 2025 2030 2035 Wage 63.7 76.8 93.2 113.2 Year 2040 2045 2050

Year 2013 2011 2012 2014 Wage 44,644 48,595 43,009 46,496 Year 2017 2015 2016 2018 Wage 50,893 58,698 53,317 55,989 Year 2019 2020 2021 Wage 61,179 63,676 66,161 Year 2012 2014 2016 2018 Wage 44.6 48.6 53.3 58.7 Year 2020 2025 2030 2035 Wage 63.7 76.8 93.2 113.2 Year 2040 2045 2050 Wage 137.6 167.1 202.5

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