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Math
CalculusCalculus: Early Transcendental Functions (MindTap Course List)6th Edition

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Chapter 1.4, Problem 11E
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Calculus: Early Transcendental Fun...

6th Edition
Ron Larson + 1 other
ISBN: 9781285774770

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
BuyFindarrow_forward

Calculus: Early Transcendental Fun...

6th Edition
Ron Larson + 1 other
ISBN: 9781285774770
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 y1, y2 and y3 represent the costs in cents per mile for gas, maintenance, and tires, respectively. (Source: Bureau of Transportation Statistics)

t y1 >2 y3
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 y1 and y3, and a quadratic model for y2.

(b) Use a graphing utility to graph y1, y2, y3, and y1 + y2+ y3 in the same viewing window. Use the model to estimate the total variable cost per mile in 2014.

(a)

To determine

The cubic model for y1 and y3 and quadratic model for y2 by the use of regression capabilities of graphing utility of the table:

ty1y2y306.93.61.717.93.91.825.94.11.837.24.11.846.55.40.759.54.90.768.94.90.7711.74.60.7810.14.60.8911.44.50.81012.34.41.0

Explanation

For y1,

Use Ti83 to find the mathematical model as below:

Step1: Press STAT then 5 then ENTER to setup the calculator’s built-in list editor.

Step2: Press STAT and ENTER to select the list editor.

Step3: Enter the data. For L1 enter the X data, here it is the values of t and for L2 enter the Y data, here it is the value of y1 as shown below:

L1L206.917.925.937.246.559.568.9711.7810.1911.41012.3

Step4: Press STAT then CALC then 6 to select the “CubicReg”.

Step5: Press ENTER to confirm.

The calculator will display the equation as:

y=ax3+bx2+cx+da=−0.0172b=0.305c=−0.867

And,

d=7.31

Hence, the cubic model of the given data is y1=−0.0172t3+0.305t2−0.87t+7.3.

For y3,

Use Ti83 to find the mathematical model as below:

Step1: Press STAT then 5 then ENTER to setup the calculator’s built-in list editor.

Step2: Press STAT and ENTER to select the list editor.

Step3: Enter the data. For L1 enter the X data, here it is the values of t and for L2 enter the Y data, here it is the value of y3 as shown below:

L1L201.711.821.831.840.750.760

(b)

To determine

To graph: The y1, y2 and y3 and y1+y2+y3 in the same window by the use of graphing utility, where, t is the year with t=0 corresponds to 2000 and the function y1, y2 and y3 represents the cost for mile for gas, maintenance and tires respectively. Also, find total variable cost per mile in 2014 by the use of model.

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Sect-1.1 P-1ESect-1.1 P-2ESect-1.1 P-3ESect-1.1 P-4ESect-1.1 P-5ESect-1.1 P-6ESect-1.1 P-7ESect-1.1 P-8ESect-1.1 P-9ESect-1.1 P-10E
Sect-1.1 P-11ESect-1.1 P-12ESect-1.1 P-13ESect-1.1 P-14ESect-1.1 P-15ESect-1.1 P-16ESect-1.1 P-17ESect-1.1 P-18ESect-1.1 P-19ESect-1.1 P-20ESect-1.1 P-21ESect-1.1 P-22ESect-1.1 P-23ESect-1.1 P-24ESect-1.1 P-25ESect-1.1 P-26ESect-1.1 P-27ESect-1.1 P-28ESect-1.1 P-29ESect-1.1 P-30ESect-1.1 P-31ESect-1.1 P-32ESect-1.1 P-33ESect-1.1 P-34ESect-1.1 P-35ESect-1.1 P-36ESect-1.1 P-37ESect-1.1 P-38ESect-1.1 P-39ESect-1.1 P-40ESect-1.1 P-41ESect-1.1 P-42ESect-1.1 P-43ESect-1.1 P-44ESect-1.1 P-45ESect-1.1 P-46ESect-1.1 P-47ESect-1.1 P-48ESect-1.1 P-49ESect-1.1 P-50ESect-1.1 P-51ESect-1.1 P-52ESect-1.1 P-53ESect-1.1 P-54ESect-1.1 P-55ESect-1.1 P-56ESect-1.1 P-57ESect-1.1 P-58ESect-1.1 P-59ESect-1.1 P-60ESect-1.1 P-61ESect-1.1 P-62ESect-1.1 P-63ESect-1.1 P-64ESect-1.1 P-65ESect-1.1 P-66ESect-1.1 P-67ESect-1.1 P-68ESect-1.1 P-69ESect-1.1 P-70ESect-1.1 P-71ESect-1.1 P-72ESect-1.1 P-73ESect-1.1 P-74ESect-1.1 P-75ESect-1.1 P-76ESect-1.1 P-77ESect-1.1 P-78ESect-1.1 P-79ESect-1.1 P-80ESect-1.2 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Find the estimated standard error for the sample mean for each of the following samples. a. n=9 with SS=1152 b....

Statistics for The Behavioral Sciences (MindTap Course List)

Write each expression as an equivalent algebric expression involving only x. (Assume x is positive.) cos(2cos1x...

Trigonometry (MindTap Course List)

In Exercises 1 to 8, find the complement of the set given that U = {0, 1, 2, 3, 4, 5, 6, 7, 8}. The set of odd ...

Mathematical Excursions (MindTap Course List)

In each of the following problems, the binomial distribution will be used. Answers may vary slightly depending ...

Understanding Basic Statistics

In Exercises 34 to 39, write a formal proof of each theorem. If the diagonals of parallelogram are perpendicula...

Elementary Geometry For College Students, 7e

A set of scores ranges from a high of X = 96 to a low of X = 27. If these scores are placed in a grouped freque...

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

Let X1, X2, and X3 represent the times necessary to perform three successive repair tasks at a certain service ...

Probability and Statistics for Engineering and the Sciences

Write each number in decimal form: 6.4101

Elementary Technical Mathematics

limx37x+65x12 = ______. a) 12 b) 75 c) 9 d) 4

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

, where E is the wedge-shaped solid shown at the right, equals:

Study Guide for Stewart's Multivariable Calculus, 8th

In Exercises 25 to 32, solve each quadratic equation by factoring. 3x2-51x+180=0 HINT: There is a common factor...

Elementary Geometry for College Students

In Exercises 516, find the inverse of the matrix, if it exists. Verify your answer. [141232123].

Finite Mathematics for the Managerial, Life, and Social Sciences

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