The following table shows the U.S. average annual wage in thousands of dollars for selected years from 2012 and projected to 2050. Suppose the rate of change of the U.S. average annual wage can be modeled by dW/dt = 1.66e^0.0395t thousand dollars per year, where t is the number of years past 2010.

(a) Use the data to find the average rates of change of the U.S. average annual wage from 2014 to 2016 and from 2016 to 2018. Which of these average rates better approximates the instantaneous rate in 2016?

(b) Use the data point from 2016 to find the function that models W(t). Use 3 significant digits.

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Average Annual Wage ($ thousands) Average Annual Wage Year Year ($ thousands) 2012 44.6 2030 93.2 2014 48.6 2035 113.2 2016 53.3 2040 137.6 2018 58.7 2045 167.1 2020 63.7 2050 202.5 2025 76.8