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CalculusCalculus: Early Transcendental Functions (MindTap Course List)Automobile CostsThe data in the table show the variable costs of operating an automobile in the United States for 2000 through 2010, where t is the year, with t = 0 corresponding to 2000. The functions y 1 , y 2 and y 3 represent the costs in cents per mile for gas, maintenance, and tires, respectively. ( Source: Bureau of Transportation Statistics ) t y 1 >2 y 3 0 6.9 3.6 1.7 1 7.9 3.9 1.8 2 5.9 4.1 1.8 3 7.2 4.1 1.8 4 6.5 5.4 0.7 5 9.5 4.9 0.7 6 8.9 4.9 0.7 7 11.7 4.6 0.7 8 10.1 4.6 0.8 9 11.4 4.5 0.8 10 12.3 4.4 1.0 (a) Use the regression capabilities of a graphing utility to find cubic models for y 1 and y 3 , and a quadratic model for y 2 . (b) Use a graphing utility to graph y 1 , y 2 , y 3 , and y 1 + y 2 + y 3 in the same viewing window. Use the model to estimate the total variable cost per mile in 2014.BuyFind*arrow_forward*

6th Edition

Ron Larson + 1 other

Publisher: Cengage Learning

ISBN: 9781285774770

Chapter 1.4, Problem 11E

Textbook Problem

Automobile CostsThe data in the table show the variable costs of operating an automobile in the United States for 2000 through 2010, where *t* is the year, with *t* = 0 corresponding to 2000. The functions y_{1}, *y*_{2} and *y*_{3} represent the costs in cents per mile for gas, maintenance, and tires, respectively. (*Source: Bureau of Transportation Statistics*)

t |
y_{1} |
>2 |
y_{3} |

0 | 6.9 | 3.6 | 1.7 |

1 | 7.9 | 3.9 | 1.8 |

2 | 5.9 | 4.1 | 1.8 |

3 | 7.2 | 4.1 | 1.8 |

4 | 6.5 | 5.4 | 0.7 |

5 | 9.5 | 4.9 | 0.7 |

6 | 8.9 | 4.9 | 0.7 |

7 | 11.7 | 4.6 | 0.7 |

8 | 10.1 | 4.6 | 0.8 |

9 | 11.4 | 4.5 | 0.8 |

10 | 12.3 | 4.4 | 1.0 |

(a) Use the regression capabilities of a graphing utility to find cubic models for *y*_{1} and y_{3}, and a quadratic model for *y*_{2}.

(b) Use a graphing utility to graph *y*_{1}, *y*_{2}, *y*_{3}, and *y*_{1} + *y*_{2}+ *y*_{3} in the same viewing window. Use the model to estimate the total variable cost per mile in 2014.

Calculus: Early Transcendental Functions (MindTap Course List)

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Finding an Inverse Function In Exercises 31-38,...Ch. 1.5 - Finding an Inverse Function In Exercises 31-38,...Ch. 1.5 - Finding an Inverse Function In Exercises 31-38,...Ch. 1.5 - Finding an Inverse Function In Exercises 39-44,...Ch. 1.5 - Finding an Inverse Function In Exercises 39-44,...Ch. 1.5 - Finding an Inverse Function In Exercises 39-44,...Ch. 1.5 - Finding an Inverse Function In Exercises 39-44,...Ch. 1.5 - Finding an Inverse Function In Exercises 39-44,...Ch. 1.5 - Finding an Inverse Function In Exercises 39-44,...Ch. 1.5 - Finding an Inverse Function In Exercises 45 and...Ch. 1.5 - Finding an Inverse Function InExercises 45 and 46,...Ch. 1.5 - Cost You need 50 pounds of two commodities costing...Ch. 1.5 - Temperature The formula C=59(F32) F459.6,...Ch. 1.5 - Testing Whether a Function Is One-to-One in...Ch. 1.5 - Testing Whether a Function Is One-to-One In...Ch. 1.5 - Testing Whether a Function Is One-to-One In...Ch. 1.5 - Testing Whether a Function Is One-to-One In...Ch. 1.5 - 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Numerical and Graphical Analysis In Exercises 87...Ch. 1.5 - Numerical and Graphical Analysis In Exercises 87...Ch. 1.5 - Missing Coordinates Determine the missing...Ch. 1.5 - HOW DO YOU SEE IT? You use a graphing utility to...Ch. 1.5 - Sketching a Graph In Exercises 91-94, sketch the...Ch. 1.5 - Sketching a Graph Sketching a Graph In Exercises...Ch. 1.5 - Sketching a Graph In Exercises 91-94, sketch the...Ch. 1.5 - Sketching a Graph In Exercises 91-94, sketch the...Ch. 1.5 - Evaluating Inverse Trigonometric Functions In...Ch. 1.5 - Evaluating Inverse Trigonometric Functions In...Ch. 1.5 - Evaluating Inverse Trigonometric Functions In...Ch. 1.5 - Evaluating Inverse Trigonometric Functions In...Ch. 1.5 - Evaluating Inverse Trigonometric Functions In...Ch. 1.5 - Evaluating Inverse Trigonometric Functions In...Ch. 1.5 - Evaluating Inverse Trigonometric Functions In...Ch. 1.5 - Evaluating Inverse Trigonometric Functions In...Ch. 1.5 - Approximating Inverse Trigonometric Functions In...Ch. 1.5 - Approximating Inverse Trigonometric Functions In...Ch. 1.5 - Approximating Inverse Trigonometric Functions In...Ch. 1.5 - Approximating Inverse Trigonometric Functions In...Ch. 1.5 - Using Properties In Exercises 107 and 108, use the...Ch. 1.5 - Using Properties In Exercises 99 and 100, use the...Ch. 1.5 - EXPLORING CONCEPTS Inverse Trigonometric Functions...Ch. 1.5 - Solving an Equation In Exercises 113-116, solve...Ch. 1.5 - Solving an Equation In Exercises 113-116, solve...Ch. 1.5 - Solving an Equation In Exercises 113-116, solve...Ch. 1.5 - Solving an Equation In Exercises 113-116, solve...Ch. 1.5 - Using a Right Triangle In Exercises 117-122, use...Ch. 1.5 - Using a Right Triangle In Exercises 117-122, use...Ch. 1.5 - Using a Right Triangle In Exercises 117-122, use...Ch. 1.5 - Using a Right Triangle In Exercises 117-122, use...Ch. 1.5 - Using a Right Triangle In Exercises 117-122, use...Ch. 1.5 - Using a Right Triangle In Exercises 117-122, use...Ch. 1.5 - Evaluating an Expression In Exercises 123-126,...Ch. 1.5 - Evaluating an Expression In Exercises 123-126,...Ch. 1.5 - Evaluating an Expression In Exercises 123-126,...Ch. 1.5 - Evaluating an Expression In Exercises 123-126,...Ch. 1.5 - Simplifying an Expression In Exercises 127-132,...Ch. 1.5 - Simplifying an Expression In Exercises 127-132,...Ch. 1.5 - Simplifying an Expression In Exercises 127-132,...Ch. 1.5 - Simplifying an Expression In Exercises 127-132,...Ch. 1.5 - Simplifying an Expression In Exercises 127-132,...Ch. 1.5 - Simplifying an Expression In Exercises 127-132,...Ch. 1.5 - Point of Intersection In Exercises 121 and 122,...Ch. 1.5 - Point of Intersection In Exercises 121 and 122,...Ch. 1.5 - Inverse Functions Describe how to find the inverse...Ch. 1.5 - Describing RelationshipsDescribe the relationship...Ch. 1.5 - Inverse Trigonometric Functions and...Ch. 1.5 - Fill in the Blank In Exercises 133 and 134, fill...Ch. 1.5 - Fill in the Blank In Exercises 133 and 134, fill...Ch. 1.5 - Verifying an Identity In Exercises 135 and 136,...Ch. 1.5 - Verifying an Identity In Exercises 135 and 136,...Ch. 1.5 - Verifying an Identity Verify each identity. (a)...Ch. 1.5 - Using an Identity Use the results of Exercise 137...Ch. 1.5 - True or False? In Exercises 139-144, determine...Ch. 1.5 - True or False? In Exercises 139-144, determine...Ch. 1.5 - arcsin2x+arccos2x=1Ch. 1.5 - True or False? In Exercises 139-144, determine...Ch. 1.5 - True or False? In Exercises 139-144, determine...Ch. 1.5 - True or False? 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Solving an Exponential or Logarithmic Equation...Ch. 1.6 - Solving an Exponential or Logarithmic Equation In...Ch. 1.6 - Solving an Inequality In Exercises 111114, solve...Ch. 1.6 - Solving an Inequality In Exercises 119-122, solve...Ch. 1.6 - Solving an Inequality In Exercises 119-122, solve...Ch. 1.6 - Solving an Inequality In Exercises 111114, solve...Ch. 1.6 - Solving an Inequality In Exercises 115 and 116,...Ch. 1.6 - Solving an Exponential or Logarithmic Equation In...Ch. 1.6 - Stating PropertiesIn your own words, stale the...Ch. 1.6 - Think About It Explain why In ex= x.Ch. 1.6 - Stating PropertiesIn your own words, stale the...Ch. 1.6 - Describe the Relationship Describe the...Ch. 1.6 - Analyze a Statement The table of values below was...Ch. 1.6 - HOW DO YOU SEE IT? 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Using the Vertical Line Test In Exercises 45 and...Ch. 1 - Using the Vertical Line Test In Exercises 4346,...Ch. 1 - Deciding Whether an Equation Is a Function In...Ch. 1 - Transformations of Functions Use a graphing...Ch. 1 - Conjecture (a) Use a graphing utility to graph the...Ch. 1 - Think About It Use the results of Exercise 48 to...Ch. 1 - Think About It What is the minimum degree of the...Ch. 1 - Writing The following graphs give the profits P...Ch. 1 - Area A wire 24 inches long is to be cut into four...Ch. 1 - Stress Test Amachine pan was tested by bending it...Ch. 1 - Median IncomeThe data in thetable show the median...Ch. 1 - Summer Olympics The table lists the U.S. media...Ch. 1 - Harmonic MotionThe motion of an oscillating weight...Ch. 1 - Finding an Inverse Function In Exercises 95-100,...Ch. 1 - Finding an Inverse Function In Exercises 95-100,...Ch. 1 - Finding an Inverse Function In Exercises 95-100,...Ch. 1 - Finding an Inverse Function In Exercises 95-100,...Ch. 1 - Finding an Inverse Function In Exercises 95-100,...Ch. 1 - Finding an Inverse Function In Exercises 95-100,...Ch. 1 - Sketching a Graph In Exercises 105 and 106, sketch...Ch. 1 - Sketching a Graph In Exercises 105 and 106, sketch...Ch. 1 - Evaluating Trigonometric Functions In Exercises...Ch. 1 - Evaluating Trigonometric Functions In Exercises...Ch. 1 - Sketching the Graph of an Exponential Function In...Ch. 1 - Sketching the Graph of an Exponential Function In...Ch. 1 - Matching In Exercises 121-124, match the function...Ch. 1 - Matching In Exercises 121-124, match the function...Ch. 1 - Matching In Exercises 121-124, match the function...Ch. 1 - Matching In Exercises 121-124, match the function...Ch. 1 - Sketching the Graph of a Logarithmic Function In...Ch. 1 - Sketching the Graph of a Logarithmic Function In...Ch. 1 - Expanding a Logarithmic Expression In Exercises...Ch. 1 - Expanding a Logarithmic Expression In Exercises...Ch. 1 - Condensing a Logarithmic Expression In Exercises...Ch. 1 - Condensing a Logarithmic Expression In Exercises...Ch. 1 - Solving an EquationIn Exercises 77 and 78, solve...Ch. 1 - Solving an Exponential or Logarithmic Equation In...Ch. 1 - Finding Inverse Functions In Exercises 79 and 80,...Ch. 1 - Finding Inverse Functions In Exercises 79 and 80,...Ch. 1 - Finding Tangent Lines Consider the circle...Ch. 1 - Finding Tangent Lines There are two tangent lines...Ch. 1 - Heaviside Function The Heaviside function H(x) is...Ch. 1 - Sketching Transformations Consider the graph of...Ch. 1 - Maximum Area A rancher plans to fence a...Ch. 1 - Maximum Area A rancher has 300 feet of fencing to...Ch. 1 - Writing a Function You are in a boat 2 miles from...Ch. 1 - Analyzing a Function Graph the function f(x)=e2ex...Ch. 1 - Slope of a Tangent Line One of the fundamental...Ch. 1 - Slope of a Tangent Line Sketch the graph of the...Ch. 1 - Composite Functions Let f(x)=11x. 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