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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 3.8, Problem 26E

(a)

To determine

**To find:** To model the given data with a fourth-degree polynomial.

Expert Solution

The fourth-degree polynomial is

**Given:**

The average age of first marriage of Japanese women has varied since 1950 is shown in table (1).

1950 | 23.00 |

1955 | 23.80 |

1960 | 24.40 |

1965 | 24.50 |

1970 | 24.20 |

1975 | 24.70 |

1980 | 25.20 |

1985 | 25.50 |

1990 | 25.90 |

1995 | 26.30 |

2000 | 27.00 |

2005 | 28.00 |

**Calculation:**

Model the given data with a fourth-degree polynomial.

Plot the graph between

Refer the figure (1).

The fourth-degree polynomial for the curve is as below.

Equate the equation (1) with equation (2).

Compare the above equation.

(b)

To determine

**To find:** The model for

Expert Solution

The value of

Calculate the value of

Differentiate equation (1) with respect to

Substitute

Thus, the value of

(c)

To determine

**To estimate:** The rate of change of marriage age for women in 1990.

Expert Solution

The rate of change of marriage age for women in 1990 is

Compute the rate of change of marriage age for women in 1990 using the formula below.

Substitute 1990 for *t*.

(d)

To determine

**To sketch:** The graph of data points and models for *A* and

Expert Solution

Plot the graph between

Calculate the difference between the year 1950 and 1955.

Substitute the value 5 for the expression

Similarly, calculate the value of

Tabulate the value of

Difference | |

0 | 0.221834 |

5.0 | 0.114614 |

10 | 0.052734 |

15.0 | 0.027194 |

20 | 0.028994 |

25.0 | 0.049134 |

30 | 0.078614 |

35.0 | 0.108434 |

40 | 0.129594 |

45.0 | 0.133094 |

50 | 0.109934 |

55.0 | 0.051114 |

60 | -0.052366 |

Plot the graph between