   Chapter 12.3, Problem 56E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Average annual wage 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 d w d t = 1.66 e 0.0395 t 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. Year Average Annual Wage ($thousands) Year Average Annual Wage ($ 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

(a)

To determine

To calculate: The average rates of change of the U.S average annual wage dWdt=1.66e0.0395t from 2014 to 2016 and from 2016 to 2018 estimates the better approximates to the instantaneous rate of average in 2016.

Explanation

Given information:

The rate of change of the U.S. average annual wage is given as dWdt=1.66e0.0395t where W is the wage in thousand dollars and t is the number of years past 2010.

The data for the annual wages for the U.S. from year 2012 to 2050 is tabulated below:

 Year Average Annual Wage ($thousands) Years Average Annual Wage ($ 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

Calculation:

Consider the provided tabulated data:

 Year Average Annual Wage ($thousands) Years Average Annual Wage ($ 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

(b)

To determine

To calculate: The function for the model W(t) for the rate of change of change of the U.S. average annual wage dWdt=1.66e0.0395t where W is the wage in thousand dollars and t is time in years.

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