Chapter 12.3, Problem 56E

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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

*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

Explanation

**Given information:**

The rate of change of the U.S. average annual wage is given as *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 | 2030 | ||

2014 | 2035 | ||

2016 | 2040 | ||

2018 | 2045 | ||

2020 | 2050 | ||

2025 |

**Calculation:**

Consider the provided tabulated data:

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

2012 | 2030 | ||

2014 | 2035 | ||

2016 | 2040 | ||

2018 | 2045 | ||

2020 | 2050 | ||

2025 |

**(b)**

To determine

**To calculate:** The function for the model *W* is the wage in thousand dollars and *t* is time in years.

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