8th Edition

ISBN: 9781337904285

Author: Larson

Publisher: CENGAGE L

Concept explainers

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These…

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are…

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) ge…

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.

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Question

Chapter 1.1, Problem 91E

To determine

To find: the years which show greatest increase and greatest decrease using slope of the graph.

Expert Solution

Answer to Problem 91E

Greatest increase in profit in years 2011 to 2012.

Greatest decrease in profit is in year 2015 to 2016.

Explanation of Solution

Given:

Following graph is given between net profits (in billions of dollars) and year where 2010 is represented as t=0

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 1.1, Problem 91E , additional homework tip 1

Formula used:

Slope of a line is given be ΔyΔx

Calculation:

Slopes of each line is calculated in table below.

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 1.1, Problem 91E , additional homework tip 2

Thus observing the slopes, it can be said that the years showing greatest increase in profit is 2011 to 2012 and the years showing greatest decrease in profit are 2015 to 2016.

Conclusion:

Slope of the given graph shows the increase or decrease in profit.

A negative slope indicates that the profit has fallen.

To determine

To find: An equation for the line between the year 2010 and 2017.

Expert Solution

Answer to Problem 91E

y=4.91x+14

Explanation of Solution

Given:

The coordinates of graph for year 2010 are (0, 14.0) and for the year 2017 are (7, 48.4)

Formula used:

Equation of a line in 2 point form is y2−y1=m(x2−x1)

Calculation:

Slope of the line is m=48.4−147−0=4.91

Now, for equation of line

y2−y1=m(x2−x1)y−14=m(x−0)y−14=4.91xy=4.91x+14

Conclusion:

The line formed between the year 2010 and 2017 is a straight line with the equation y=4.91x+14 .

(c)

To determine

To interpret: the meaning of slope from point (b).

(c)

Expert Solution

Answer to Problem 91E

A positive slope indicating an overall increase in profit over the years.

Explanation of Solution

Given:

The equation of the line is y=4.91x+14 with a slope of 4.91

In an equation of a line a slope means the change in value on y-axis compared to change in value on x-axis.

A positive slope indicates that the value on y-axis is increasing faster as compared to increase in value on x-axis.

In the equation, the slope is 4.91 which means on an average there has been an increase in profit of 4.91 billions of dollars each year.

Conclusion:

A positive slope indicates that there has been an increase in profit each year on an average basis.

To determine

To find: estimated net profit in the year 2021 using the equation from part (b) and whether it is accurate.

Expert Solution

Answer to Problem 91E

68.01 billions of dollars.

It may be inaccurate.

Explanation of Solution

Given:

The equation of the line is y=4.91x+14 .

For the year 2021 x is to be considered as x=11 because of designation stated in the question.

Calculation:

y=4.91x+14y=4.91(11)+14y=54.01+14y=68.01 .

Conclusion:

On solving the equation, the estimated net profit will be 68.01.

However, one cannot claim the accuracy of this estimate because it is found out using the average increase in profit formula.

The equation used is not an actual equation of the profit, but rather found from the average increase.

One must not forget, that there were many lines in the data given with unequal slope, indicating the unpredictability of the graph.

So, the estimated profit may be correct or incorrect.

Chapter 1.1, Problem 90E

Chapter 1.1, Problem 92E

Chapter 1 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

Ch. 1.1 - Prob. 1E Ch. 1.1 - Prob. 2E Ch. 1.1 - Prob. 3E Ch. 1.1 - Prob. 4E Ch. 1.1 - Prob. 5E Ch. 1.1 - Prob. 6E Ch. 1.1 - Prob. 7E Ch. 1.1 - Prob. 8E Ch. 1.1 - Prob. 9E Ch. 1.1 - Prob. 10E

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Prob. 29E Ch. 1.6 - Prob. 30E Ch. 1.6 - Prob. 31E Ch. 1.6 - Prob. 32E Ch. 1.6 - Prob. 33E Ch. 1.6 - Prob. 34E Ch. 1.6 - Prob. 35E Ch. 1.6 - Prob. 36E Ch. 1.6 - Prob. 37E Ch. 1.6 - Prob. 38E Ch. 1.6 - Prob. 39E Ch. 1.6 - Prob. 40E Ch. 1.6 - Prob. 41E Ch. 1.6 - Prob. 42E Ch. 1.6 - Prob. 43E Ch. 1.6 - Prob. 44E Ch. 1.6 - Prob. 45E Ch. 1.6 - Prob. 46E Ch. 1.6 - Prob. 47E Ch. 1.6 - Prob. 48E Ch. 1.6 - Prob. 49E Ch. 1.6 - Prob. 50E Ch. 1.6 - Prob. 51E Ch. 1.6 - Prob. 52E Ch. 1.6 - Prob. 53E Ch. 1.6 - Prob. 54E Ch. 1.6 - Prob. 55E Ch. 1.6 - Prob. 56E Ch. 1.6 - Prob. 57E Ch. 1.6 - Prob. 58E Ch. 1.6 - Prob. 59E Ch. 1.6 - Prob. 60E Ch. 1.6 - Prob. 61E Ch. 1.6 - Prob. 62E Ch. 1.6 - Prob. 63E Ch. 1.6 - Prob. 64E Ch. 1.6 - Prob. 65E Ch. 1.6 - Prob. 66E Ch. 1.6 - Prob. 67E Ch. 1.6 - Prob. 68E Ch. 1.6 - Prob. 69E Ch. 1.6 - Prob. 70E Ch. 1.6 - Prob. 71E Ch. 1.6 - Prob. 72E Ch. 1.6 - Prob. 73E Ch. 1.6 - Prob. 74E Ch. 1.6 - Prob. 75E Ch. 1.6 - Prob. 76E Ch. 1.6 - Prob. 77E Ch. 1.6 - Prob. 78E Ch. 1.6 - Prob. 79E Ch. 1.6 - Prob. 80E Ch. 1.6 - Prob. 81E Ch. 1.6 - Prob. 82E Ch. 1.6 - Prob. 83E Ch. 1.6 - Prob. 84E Ch. 1.6 - Prob. 85E Ch. 1.6 - Prob. 86E Ch. 1.6 - Prob. 87E Ch. 1.6 - Prob. 88E Ch. 1.6 - Prob. 89E Ch. 1.6 - Prob. 90E Ch. 1.6 - Prob. 91E Ch. 1.6 - Prob. 92E Ch. 1.6 - Prob. 93E Ch. 1.6 - Prob. 94E Ch. 1.6 - Prob. 95E Ch. 1.6 - Prob. 96E Ch. 1.6 - Prob. 97E Ch. 1.6 - Prob. 98E Ch. 1.6 - Prob. 99E Ch. 1.6 - Prob. 100E Ch. 1.6 - Prob. 101E Ch. 1.6 - Prob. 102E Ch. 1.6 - Prob. 103E Ch. 1.6 - Prob. 104E Ch. 1.6 - Prob. 105E Ch. 1.6 - Prob. 106E Ch. 1.6 - Prob. 107E Ch. 1.6 - Prob. 108E Ch. 1.6 - Prob. 109E Ch. 1.6 - Prob. 110E Ch. 1.6 - Prob. 111E Ch. 1.6 - Prob. 112E Ch. 1.6 - Prob. 113E Ch. 1.6 - Prob. 114E Ch. 1.6 - Prob. 115E Ch. 1.6 - Prob. 116E Ch. 1.6 - Prob. 117E Ch. 1.6 - Prob. 118E Ch. 1.6 - Prob. 119E Ch. 1.6 - Prob. 120E Ch. 1.6 - Prob. 121E Ch. 1.6 - Prob. 122E Ch. 1.6 - Prob. 123E Ch. 1.6 - Prob. 124E Ch. 1.6 - Prob. 125E Ch. 1.6 - Prob. 126E Ch. 1.6 - Prob. 127E Ch. 1.6 - Prob. 128E Ch. 1.6 - Prob. 129E Ch. 1.6 - Prob. 130E Ch. 1.6 - Prob. 131E Ch. 1.6 - Prob. 132E Ch. 1.6 - Prob. 133E Ch. 1.6 - Prob. 134E Ch. 1.6 - Prob. 135E Ch. 1.6 - Prob. 136E Ch. 1.6 - Prob. 137E Ch. 1.6 - Prob. 138E Ch. 1.6 - Prob. 139E Ch. 1.6 - Prob. 140E Ch. 1.6 - Prob. 141E Ch. 1.6 - Prob. 142E Ch. 1.6 - Prob. 143E Ch. 1.6 - Prob. 144E Ch. 1.7 - Prob. 1E Ch. 1.7 - Prob. 2E Ch. 1.7 - Prob. 3E Ch. 1.7 - Prob. 4E Ch. 1.7 - Prob. 5E Ch. 1.7 - Prob. 6E Ch. 1.7 - Prob. 7E Ch. 1.7 - Prob. 8E Ch. 1.7 - Prob. 9E Ch. 1.7 - Prob. 10E Ch. 1.7 - Prob. 11E Ch. 1.7 - Prob. 12E Ch. 1.7 - Prob. 13E Ch. 1.7 - Prob. 14E Ch. 1.7 - Prob. 15E Ch. 1.7 - Prob. 16E Ch. 1.7 - Prob. 17E Ch. 1.7 - Prob. 18E Ch. 1.7 - Prob. 19E Ch. 1.7 - Prob. 20E Ch. 1.7 - Prob. 21E Ch. 1.7 - Prob. 22E Ch. 1.7 - Prob. 23E Ch. 1.7 - Prob. 24E Ch. 1.7 - Prob. 25E Ch. 1.7 - Prob. 26E Ch. 1.7 - Prob. 27E Ch. 1.7 - Prob. 28E Ch. 1.7 - Prob. 29E Ch. 1.7 - Prob. 30E Ch. 1.7 - Prob. 31E Ch. 1.7 - Prob. 32E Ch. 1.7 - Prob. 33E Ch. 1.7 - Prob. 34E Ch. 1 - Prob. 1CR Ch. 1 - Prob. 2CR Ch. 1 - Prob. 3CR Ch. 1 - Prob. 4CR Ch. 1 - Prob. 5CR Ch. 1 - Prob. 6CR Ch. 1 - Prob. 7CR Ch. 1 - Prob. 8CR Ch. 1 - Prob. 9CR Ch. 1 - Prob. 10CR Ch. 1 - Prob. 11CR Ch. 1 - Prob. 12CR Ch. 1 - Prob. 13CR Ch. 1 - Prob. 14CR Ch. 1 - Prob. 15CR Ch. 1 - Prob. 16CR Ch. 1 - Prob. 17CR Ch. 1 - Prob. 18CR Ch. 1 - Prob. 19CR Ch. 1 - Prob. 20CR Ch. 1 - Prob. 21CR Ch. 1 - Prob. 22CR Ch. 1 - Prob. 23CR Ch. 1 - Prob. 24CR Ch. 1 - Prob. 25CR Ch. 1 - Prob. 26CR Ch. 1 - Prob. 27CR Ch. 1 - Prob. 28CR Ch. 1 - Prob. 29CR Ch. 1 - Prob. 30CR Ch. 1 - Prob. 31CR Ch. 1 - Prob. 32CR Ch. 1 - Prob. 33CR Ch. 1 - Prob. 34CR Ch. 1 - Prob. 35CR Ch. 1 - Prob. 36CR Ch. 1 - Prob. 37CR Ch. 1 - Prob. 38CR Ch. 1 - Prob. 39CR Ch. 1 - Prob. 40CR Ch. 1 - Prob. 41CR Ch. 1 - Prob. 42CR Ch. 1 - Prob. 43CR Ch. 1 - Prob. 44CR Ch. 1 - Prob. 45CR Ch. 1 - Prob. 46CR Ch. 1 - Prob. 47CR Ch. 1 - Prob. 48CR Ch. 1 - Prob. 49CR Ch. 1 - Prob. 50CR Ch. 1 - Prob. 51CR Ch. 1 - Prob. 52CR Ch. 1 - Prob. 53CR Ch. 1 - Prob. 54CR Ch. 1 - Prob. 55CR Ch. 1 - Prob. 56CR Ch. 1 - Prob. 57CR Ch. 1 - Prob. 58CR Ch. 1 - Prob. 59CR Ch. 1 - Prob. 60CR Ch. 1 - Prob. 61CR Ch. 1 - Prob. 62CR Ch. 1 - Prob. 63CR Ch. 1 - Prob. 64CR Ch. 1 - Prob. 65CR Ch. 1 - Prob. 66CR Ch. 1 - Prob. 67CR Ch. 1 - Prob. 68CR Ch. 1 - Prob. 69CR Ch. 1 - Prob. 70CR Ch. 1 - Prob. 71CR Ch. 1 - Prob. 72CR Ch. 1 - Prob. 73CR Ch. 1 - Prob. 74CR Ch. 1 - Prob. 75CR Ch. 1 - Prob. 76CR Ch. 1 - Prob. 77CR Ch. 1 - Prob. 78CR Ch. 1 - Prob. 79CR Ch. 1 - Prob. 80CR Ch. 1 - Prob. 81CR Ch. 1 - Prob. 82CR Ch. 1 - Prob. 83CR Ch. 1 - Prob. 84CR Ch. 1 - Prob. 85CR Ch. 1 - Prob. 86CR Ch. 1 - Prob. 87CR Ch. 1 - Prob. 88CR Ch. 1 - Prob. 89CR Ch. 1 - Prob. 90CR Ch. 1 - Prob. 91CR Ch. 1 - Prob. 92CR Ch. 1 - Prob. 93CR Ch. 1 - Prob. 94CR Ch. 1 - Prob. 95CR Ch. 1 - Prob. 96CR Ch. 1 - Prob. 97CR Ch. 1 - Prob. 98CR Ch. 1 - Prob. 99CR Ch. 1 - Prob. 100CR Ch. 1 - Prob. 101CR Ch. 1 - Prob. 102CR Ch. 1 - Prob. 103CR Ch. 1 - Prob. 104CR Ch. 1 - Prob. 105CR Ch. 1 - Prob. 106CR Ch. 1 - Prob. 107CR Ch. 1 - Prob. 108CR Ch. 1 - Prob. 109CR Ch. 1 - Prob. 110CR Ch. 1 - Prob. 1CT Ch. 1 - Prob. 2CT Ch. 1 - Prob. 3CT Ch. 1 - Prob. 4CT Ch. 1 - Prob. 5CT Ch. 1 - Prob. 6CT Ch. 1 - Prob. 7CT Ch. 1 - Prob. 8CT Ch. 1 - Prob. 9CT Ch. 1 - Prob. 10CT Ch. 1 - Prob. 11CT Ch. 1 - Prob. 12CT Ch. 1 - Prob. 13CT Ch. 1 - Prob. 14CT Ch. 1 - Prob. 15CT Ch. 1 - Prob. 16CT Ch. 1 - Prob. 17CT Ch. 1 - Prob. 18CT Ch. 1 - Prob. 19CT Ch. 1 - Prob. 20CT

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