Chapter 10.1, Problem 64E

BuyFind*arrow_forward*

11th Edition

Ronald J. Harshbarger + 1 other

ISBN: 9781305108042

Textbook Problem

**Modeling Energy from crude oil** The table shows the total energy supply from crude oil products, in quadrillion BTUs, for selected years from 2010 and projected to 2040.

(a) Find the cubic function that is the best model for the data. Use *x* as the number of years after 2010 and *C(x)* as the quadrillion BTUs of energy from crude oil products. Report the model with three significant digit coefficients.

(b) Find the critical values of the reported model.

(c) Find the reported model’s critical points and classify them.

(d) Do you think this model will be valid for years past 2040? Explain.

Total Energy Supply from Crude Oil Products (in quadrillion BTUs) |
|||

Year | BTUs | Year |
BTUs |

2010 | 11.6 | 2030 | 13.5 |

2015 | 15.6 | 2035 | 13.4 |

2020 | 16.0 | 2040 | 13.1 |

2025 | 14.5 |

*Source:* U.S. Energy Information Administration

**(a)**

To determine

The cubic function that best models the size of this data, where *x* is the number of years after 2010, if the following table shows the total energy supply from crude oil products, in quadrillion BTUs, for selected years from 2010 to 2040.

Year |
BTU |
Year |
BTU |

2010 | 11.6 | 2030 | 13.5 |

2015 | 15.6 | 2035 | 13.4 |

2020 | 16.0 | 2040 | 13.1 |

2025 | 14.5 |

Explanation

**Given Information:**

The provided table is:

Year |
BTU |
Year |
BTU |

2010 | 11.6 | 2030 | 13.5 |

2015 | 15.6 | 2035 | 13.4 |

2020 | 16.0 | 2040 | 13.1 |

2025 | 14.5 |

**Explanation:**

The critical values are the only values at which the graph can have turning points, the derivative cannot change sign anywhere except at the critical value.

This, in an interval between two critical values, the sign of the derivative at any value in the interval will be the sign of the derivative at all values in the interval...

**(b)**

To determine

**To calculate:** The critical values of the data if the following table shows the total energy supply from crude oil products, in quadrillion BTUs, for selected years from 2010 to 2040.

Year |
BTU |
Year |
BTU |

2010 | 11.6 | 2030 | 13.5 |

2015 | 15.6 | 2035 | 13.4 |

2020 | 16.0 | 2040 | 13.1 |

2025 | 14.5 |

**(c)**

To determine

**To calculate:** The critical points of the data and also classify them, if the following table shows the total energy supply from crude oil products, in quadrillion BTUs, for selected years from 2010 to 2040.

Year |
BTU |
Year |
BTU |

2010 | 11.6 | 2030 | 13.5 |

2015 | 15.6 | 2035 | 13.4 |

2020 | 16.0 | 2040 | 13.1 |

2025 | 14.5 |

**(d)**

To determine

If this model will be valid till 2040 if the following table shows the total energy supply from crude oil products, in quadrillion BTUs, for selected years from 2010 to 2040.

Year |
BTU |
Year |
BTU |

2010 | 11.6 | 2030 | 13.5 |

2015 | 15.6 | 2035 | 13.4 |

2020 | 16.0 | 2040 | 13.1 |

2025 | 14.5 |

Sect-10.1 P-1CPSect-10.1 P-2CPSect-10.1 P-3CPSect-10.1 P-4CPSect-10.1 P-1ESect-10.1 P-2ESect-10.1 P-3ESect-10.1 P-4ESect-10.1 P-5ESect-10.1 P-6E

Sect-10.1 P-7ESect-10.1 P-8ESect-10.1 P-9ESect-10.1 P-10ESect-10.1 P-11ESect-10.1 P-12ESect-10.1 P-13ESect-10.1 P-14ESect-10.1 P-15ESect-10.1 P-16ESect-10.1 P-17ESect-10.1 P-18ESect-10.1 P-19ESect-10.1 P-20ESect-10.1 P-21ESect-10.1 P-22ESect-10.1 P-23ESect-10.1 P-24ESect-10.1 P-25ESect-10.1 P-26ESect-10.1 P-27ESect-10.1 P-28ESect-10.1 P-29ESect-10.1 P-30ESect-10.1 P-31ESect-10.1 P-32ESect-10.1 P-33ESect-10.1 P-34ESect-10.1 P-35ESect-10.1 P-36ESect-10.1 P-37ESect-10.1 P-38ESect-10.1 P-39ESect-10.1 P-40ESect-10.1 P-41ESect-10.1 P-42ESect-10.1 P-43ESect-10.1 P-44ESect-10.1 P-45ESect-10.1 P-46ESect-10.1 P-47ESect-10.1 P-48ESect-10.1 P-49ESect-10.1 P-50ESect-10.1 P-51ESect-10.1 P-52ESect-10.1 P-53ESect-10.1 P-54ESect-10.1 P-55ESect-10.1 P-56ESect-10.1 P-57ESect-10.1 P-58ESect-10.1 P-59ESect-10.1 P-60ESect-10.1 P-61ESect-10.1 P-62ESect-10.1 P-63ESect-10.1 P-64ESect-10.1 P-65ESect-10.2 P-1CPSect-10.2 P-2CPSect-10.2 P-3CPSect-10.2 P-4CPSect-10.2 P-1ESect-10.2 P-2ESect-10.2 P-3ESect-10.2 P-4ESect-10.2 P-5ESect-10.2 P-6ESect-10.2 P-7ESect-10.2 P-8ESect-10.2 P-9ESect-10.2 P-10ESect-10.2 P-11ESect-10.2 P-12ESect-10.2 P-13ESect-10.2 P-14ESect-10.2 P-15ESect-10.2 P-16ESect-10.2 P-17ESect-10.2 P-18ESect-10.2 P-19ESect-10.2 P-20ESect-10.2 P-21ESect-10.2 P-22ESect-10.2 P-23ESect-10.2 P-24ESect-10.2 P-25ESect-10.2 P-26ESect-10.2 P-27ESect-10.2 P-28ESect-10.2 P-29ESect-10.2 P-30ESect-10.2 P-31ESect-10.2 P-32ESect-10.2 P-33ESect-10.2 P-34ESect-10.2 P-35ESect-10.2 P-36ESect-10.2 P-37ESect-10.2 P-38ESect-10.2 P-39ESect-10.3 P-1CPSect-10.3 P-2CPSect-10.3 P-3CPSect-10.3 P-4CPSect-10.3 P-1ESect-10.3 P-2ESect-10.3 P-3ESect-10.3 P-5ESect-10.3 P-6ESect-10.3 P-7ESect-10.3 P-8ESect-10.3 P-9ESect-10.3 P-10ESect-10.3 P-11ESect-10.3 P-12ESect-10.3 P-13ESect-10.3 P-14ESect-10.3 P-15ESect-10.3 P-16ESect-10.3 P-17ESect-10.3 P-18ESect-10.3 P-19ESect-10.3 P-20ESect-10.3 P-21ESect-10.3 P-22ESect-10.3 P-23ESect-10.3 P-24ESect-10.3 P-25ESect-10.3 P-26ESect-10.3 P-27ESect-10.3 P-28ESect-10.3 P-29ESect-10.3 P-30ESect-10.3 P-33ESect-10.3 P-34ESect-10.3 P-35ESect-10.3 P-36ESect-10.3 P-37ESect-10.3 P-38ESect-10.3 P-39ESect-10.3 P-40ESect-10.3 P-41ESect-10.3 P-42ESect-10.3 P-43ESect-10.3 P-47ESect-10.3 P-48ESect-10.3 P-49ESect-10.4 P-1CPSect-10.4 P-2CPSect-10.4 P-3CPSect-10.4 P-1ESect-10.4 P-2ESect-10.4 P-3ESect-10.4 P-4ESect-10.4 P-5ESect-10.4 P-6ESect-10.4 P-7ESect-10.4 P-8ESect-10.4 P-9ESect-10.4 P-10ESect-10.4 P-11ESect-10.4 P-12ESect-10.4 P-13ESect-10.4 P-14ESect-10.4 P-15ESect-10.4 P-16ESect-10.4 P-17ESect-10.4 P-18ESect-10.4 P-19ESect-10.4 P-20ESect-10.4 P-21ESect-10.4 P-22ESect-10.4 P-23ESect-10.4 P-24ESect-10.4 P-25ESect-10.4 P-26ESect-10.4 P-27ESect-10.4 P-28ESect-10.4 P-29ESect-10.4 P-30ESect-10.4 P-31ESect-10.4 P-32ESect-10.4 P-33ESect-10.5 P-1CPSect-10.5 P-2CPSect-10.5 P-1ESect-10.5 P-2ESect-10.5 P-3ESect-10.5 P-4ESect-10.5 P-5ESect-10.5 P-6ESect-10.5 P-7ESect-10.5 P-8ESect-10.5 P-9ESect-10.5 P-10ESect-10.5 P-11ESect-10.5 P-12ESect-10.5 P-13ESect-10.5 P-14ESect-10.5 P-15ESect-10.5 P-16ESect-10.5 P-17ESect-10.5 P-18ESect-10.5 P-19ESect-10.5 P-20ESect-10.5 P-21ESect-10.5 P-22ESect-10.5 P-23ESect-10.5 P-24ESect-10.5 P-25ESect-10.5 P-26ESect-10.5 P-27ESect-10.5 P-28ESect-10.5 P-29ESect-10.5 P-30ESect-10.5 P-31ESect-10.5 P-32ESect-10.5 P-33ESect-10.5 P-34ESect-10.5 P-35ESect-10.5 P-36ESect-10.5 P-37ESect-10.5 P-38ESect-10.5 P-39ESect-10.5 P-40ESect-10.5 P-41ESect-10.5 P-42ESect-10.5 P-43ECh-10 P-1RECh-10 P-2RECh-10 P-3RECh-10 P-4RECh-10 P-5RECh-10 P-6RECh-10 P-7RECh-10 P-8RECh-10 P-9RECh-10 P-10RECh-10 P-11RECh-10 P-12RECh-10 P-13RECh-10 P-14RECh-10 P-15RECh-10 P-16RECh-10 P-17RECh-10 P-18RECh-10 P-19RECh-10 P-20RECh-10 P-21RECh-10 P-22RECh-10 P-23RECh-10 P-24RECh-10 P-25RECh-10 P-26RECh-10 P-27RECh-10 P-28RECh-10 P-29RECh-10 P-30RECh-10 P-31RECh-10 P-32RECh-10 P-33RECh-10 P-34RECh-10 P-35RECh-10 P-36RECh-10 P-37RECh-10 P-38RECh-10 P-39RECh-10 P-40RECh-10 P-41RECh-10 P-42RECh-10 P-43RECh-10 P-44RECh-10 P-45RECh-10 P-46RECh-10 P-47RECh-10 P-48RECh-10 P-49RECh-10 P-50RECh-10 P-51RECh-10 P-52RECh-10 P-53RECh-10 P-54RECh-10 P-55RECh-10 P-1TCh-10 P-2TCh-10 P-3TCh-10 P-4TCh-10 P-5TCh-10 P-6TCh-10 P-7TCh-10 P-8TCh-10 P-9TCh-10 P-10TCh-10 P-11TCh-10 P-12TCh-10 P-13TCh-10 P-14TCh-10 P-15TCh-10 P-16TCh-10 P-17T

Finite Mathematics

Calculus: Early Transcendental Functions

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Statistics for The Behavioral Sciences (MindTap Course List)

Calculus: Early Transcendentals

Calculus (MindTap Course List)

Probability and Statistics for Engineering and the Sciences

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Calculus: An Applied Approach (MindTap Course List)

Multivariable Calculus

Single Variable Calculus

Essentials Of Statistics

Applied Calculus

Understanding Basic Statistics

Precalculus: Mathematics for Calculus (Standalone Book)

Finite Mathematics and Applied Calculus (MindTap Course List)

Single Variable Calculus: Early Transcendentals, Volume I

Intermediate Algebra

Mathematical Excursions (MindTap Course List)

Elementary Technical Mathematics

Elements Of Modern Algebra

Contemporary Mathematics for Business & Consumers

Trigonometry (MindTap Course List)

Elementary Geometry For College Students, 7e

Finite Mathematics for the Managerial, Life, and Social Sciences

Elementary Geometry for College Students

Calculus of a Single Variable

Single Variable Calculus: Early Transcendentals

Calculus: Early Transcendental Functions (MindTap Course List)

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Introduction To Statistics And Data Analysis

Study Guide for Stewart's Multivariable Calculus, 8th

Mathematics For Machine Technology

Statistics for Business & Economics, Revised (MindTap Course List)

Calculus (MindTap Course List)

Research Methods for the Behavioral Sciences (MindTap Course List)

Multivariable Calculus

Research Methods for the Behavioral Sciences (MindTap Course List)

STATISTICS F/BUSINESS+ECONOMICS-TEXT

College Algebra (MindTap Course List)