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Mathematical Applications for the Management, Life, and Social Sciences11th Edition

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Chapter 13.1, Problem 34E
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Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

Solutions

Chapter
Section
Problem 1CP
Problem 2CP
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
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
BuyFindarrow_forward

Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

Oil imports Crude oil and petroleum products are imported continuously by the United States. The following table and figure show the net expenditures for U.S. oil imports for selected years (in billions of dollars per year) (Source: Energy Information Administration), (a) Use n = 5 equal subdivisions and left-hand end-points to estimate the area under the graph from 2014 to 2024.

(b) What does this area represent in terms of U.S. oil imports?

Year Billions of Dollars
2014 219.5
2016 192.0
2018 191.0
2020 198.9
2022 214.5
2024 228.4

Chapter 13.1, Problem 34E, 34. Oil imports Crude oil and petroleum products are imported continuously by the United States. The

(a)

To determine

To calculate: The area under the curve in the graph using n=5 equal subdivisions and left-hand endpoints from 2014 to 2024 where the graph shows the net expenditures for U.S. oil imports.

Mathematical Applications for the Management, Life, and Social Sciences, Chapter 13.1, Problem 34E , additional homework tip 1

Explanation

Given Information:

The provided graph and table are,

Years Billions Of Dollars
2014 219.5
2016 192
2018 191
2020 198.9
2022 214.5
2024 228.4

Formula used:

The base of the rectangles to approximate the area is b−an where the interval [a,b] on which function is defined is divided into n subintervals.

The height of the rectangles is the value of the function calculated at the left-hand end point of the interval containing the base.

The area of a rectangle is base×height.

The approximated area under the curve is sum of the areas of each rectangle.

Calculation:

Consider the provided table and graph,

Years Billions Of Dollars
2014 219.5
2016 192
2018 191
2020 198.9
2022 214.5
2024 228.4

Since, the table represents the corresponding values of y at various x.

Thus, the height of the function from 2014 to 2024 is 219.5, 192, 191, 198.9 and 214.5 respectively.

The base of the rectangles to approximate the area is b−an where the interval [a,b] on which function is defined is divided into n subintervals

(b)

To determine

What the area under the curve in the graph represents where the graph shows the net expenditures for U.S. oil imports.

Mathematical Applications for the Management, Life, and Social Sciences, Chapter 13.1, Problem 34E , additional homework tip 2

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