Mathematical Excursions (MindTap Course List)
4th Edition
ISBN: 9781305965584
Author: Richard N. Aufmann, Joanne Lockwood, Richard D. Nation, Daniel K. Clegg
Publisher: Cengage Learning
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Chapter 4.1, Problem 32ES
To determine
According to the
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31.
On Feb. 8, this year, at 6am in the morning all UiB meteorology professors met to discuss a highly unfortunate
and top-urgent crisis: Their most precious instrument, responsible for measuring the air temperature hour-by-
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up-to-date air temperature readings? Silent devastation - and maybe a hint of panic, also - hung in the room.
Apprentice Taylor, who - as always - was late to the meeting, sensed that this was his chance to shine! Could
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Consider a forest where the population of a particular plant species grows exponentially. In a real-world
scenario, we often deal with systems where the analytical function describing the phenomenon is not available.
In such cases, numerical methods come in handy.
For the sake of this task, however, you are provided with an analytical function so that you can compare
the results of the numerical methods to some ground truth. The population P(t) of the plants at time t (in
years) is given by the equation:
P(t) = 200
0.03 t
You are tasked with estimating the rate of change of the plant population at t = 5 years using numerical
differentiation methods. First, compute the value of P'(t) at t = 5 analytically. Then, estimate P'(t) at t = 5
years using the following numerical differentiation methods:
⚫ forward difference method (2nd-order accurate)
3
⚫ backward difference method (2nd-order accurate)
⚫ central difference method (2nd-order accurate)
Use h = 0.5 as the step size and round all…
Chapter 4 Solutions
Mathematical Excursions (MindTap Course List)
Ch. 4.1 - Verify this apportionment using the Jefferson...Ch. 4.1 - Find the apportionment that would have resulted if...Ch. 4.1 - Prob. 3EECh. 4.1 - Find the apportionment that would have resulted if...Ch. 4.1 - Explain how to calculate the standard divisor of...Ch. 4.1 - Teacher Aides A total of 25 teacher aides are to...Ch. 4.1 - In the Hamilton apportionment method, explain how...Ch. 4.1 - Prob. 4ESCh. 4.1 - Governing Boards The following table shows how the...Ch. 4.1 - Forest Rangers The table below shows how the...
Ch. 4.1 - Sales Associates The table below shows the number...Ch. 4.1 - Hospital Interns The table below shows the number...Ch. 4.1 - House of Representatives The U.S. House of...Ch. 4.1 - College Enrollment The following table shows the...Ch. 4.1 - Medical Care A hospital district consists of six...Ch. 4.1 - What is the Alabama paradox?Ch. 4.1 - What is the population paradox?Ch. 4.1 - What is the new states paradox?Ch. 4.1 - 15. What is the Balinski-Young Impossibility...Ch. 4.1 - Apportionment of Projectors Consider the...Ch. 4.1 - Hotel Management A company operates four resorts....Ch. 4.1 - Prob. 18ESCh. 4.1 - Management Scientific Research Corporation has...Ch. 4.1 - Prob. 20ESCh. 4.1 - Elementary School Teachers The following table...Ch. 4.1 - Social Workers The following table shows the...Ch. 4.1 - Computer Usage The table below shows the number of...Ch. 4.1 - The population of Illinois increased by over...Ch. 4.1 - Prob. 25ESCh. 4.1 - Prob. 26ESCh. 4.1 - Computer Usage Use the Webster method to apportion...Ch. 4.1 - Demographics The table below shows the populations...Ch. 4.1 - Which of she following apportionment methods can...Ch. 4.1 - According to Michael Balinski and H. Peyton Young,...Ch. 4.1 - 31. What method is presently used to apportion the...Ch. 4.1 - Prob. 32ESCh. 4.1 - John Quincy Adams, the sixth president of the...Ch. 4.1 - In the Huntington-Hill method of apportionment,...Ch. 4.1 - Prob. 35ESCh. 4.2 - Using the Borda method of voting, which flavor of...Ch. 4.2 - Instead of using the normal Borda method, suppose...Ch. 4.2 - Prob. 3EECh. 4.2 - Suppose the Borda method used in Exercise I of...Ch. 4.2 - Prob. 5EECh. 4.2 - Can the assignment of points for first. Second,...Ch. 4.2 - Prob. 7EECh. 4.2 - Prob. 1ESCh. 4.2 - Explain why the plurality voting system may not be...Ch. 4.2 - Prob. 3ESCh. 4.2 - Explain how the plurality with elimination voting...Ch. 4.2 - Prob. 5ESCh. 4.2 - Prob. 6ESCh. 4.2 - Is there a best voting method? Is one method more...Ch. 4.2 - Explain why. if only two candidates are running,...Ch. 4.2 - Presidential Election The table below shows the...Ch. 4.2 - Breakfast Cereal Sixteen people were asked to rank...Ch. 4.2 - Cartoon Characters A kindergarten class was...Ch. 4.2 - Catering A 15-person committee is having lunch...Ch. 4.2 - Movies Fifty consumers were surveyed about their...Ch. 4.2 - Breakfast Cereal Use the Borda count method of...Ch. 4.2 - Prob. 15ESCh. 4.2 - Catering Use the Borda count method of voting to...Ch. 4.2 - Class Election A senior high school class held an...Ch. 4.2 - Cell Phone Usage A journalist reviewing various...Ch. 4.2 - Baseball Uniforms A Little League baseball team...Ch. 4.2 - Radio Stations A number of college students were...Ch. 4.2 - Class Election Use plurality with elimination to...Ch. 4.2 - Prob. 22ESCh. 4.2 - Campus Club A campus club has money left over in...Ch. 4.2 - Recreation A company is planning its annual summer...Ch. 4.2 - X-Men Movies Fans of the X-Men movies have been...Ch. 4.2 - Prob. 26ESCh. 4.2 - School Mascot A new college needs to pick a moscot...Ch. 4.2 - Election Five candidates are running for president...Ch. 4.2 - Prob. 29ESCh. 4.2 - Radio Stations Use the pairwise comparison method...Ch. 4.2 - Does the winner in Exercise tic satisfy the...Ch. 4.2 - 32. Does the winner in Exercise 12 satisfy the...Ch. 4.2 - Prob. 33ESCh. 4.2 - Prob. 34ESCh. 4.2 - Prob. 35ESCh. 4.2 - Prob. 36ESCh. 4.2 - Election Three candidates are running for mayor. A...Ch. 4.2 - Film Competition Three films have been selected as...Ch. 4.2 - 39. Election A campus club needs to elect four...Ch. 4.2 - Scholarship Awards The members of a scholarship...Ch. 4.2 - Another method of voting is to assign a weight. or...Ch. 4.2 - Prob. 42ESCh. 4.2 - Prob. 43ESCh. 4.3 - Using the data in Example 1 on page 211, list all...Ch. 4.3 - For the data in Example I on page 211, calculate...Ch. 4.3 - Prob. 3EECh. 4.3 - Prob. 4EECh. 4.3 - Create a voting system with three members that is...Ch. 4.3 - Prob. 6EECh. 4.3 - Prob. 7EECh. 4.3 - In the following exercises that involve weighted...Ch. 4.3 - In the following exercises that involve weighted...Ch. 4.3 - Prob. 3ESCh. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Prob. 8ESCh. 4.3 - Prob. 9ESCh. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Prob. 13ESCh. 4.3 - Prob. 14ESCh. 4.3 - Music Education A music department Consists of a...Ch. 4.3 - Prob. 16ESCh. 4.3 - Criminal Justice In a criminal trial, each of the...Ch. 4.3 - Criminal Justice In California civil court cases,...Ch. 4.3 - Identify any dictator and all dummies for each...Ch. 4.3 - Identify any dictator and all dummies for each...Ch. 4.3 - Prob. 21ESCh. 4.3 - Prob. 22ESCh. 4.3 - Football At the beginning of each football season,...Ch. 4.3 - Prob. 24ESCh. 4.3 - Prob. 25ESCh. 4.3 - Prob. 26ESCh. 4.3 - Consider the weighted voting system { q:8,3,3,2 },...Ch. 4.3 - Prob. 28ESCh. 4.3 - Prob. 29ESCh. 4.3 - UN Security Council The United Nations C Security...Ch. 4 - Education The following table shows the...Ch. 4 - Airline Industry The following table shows the...Ch. 4 - Airline Industry The table below shows how the...Ch. 4 - 4. Education The following table shows the number...Ch. 4 - Technology A company has four offices. The...Ch. 4 - Automobile Sales Consider the apportionment of 27...Ch. 4 - Music Company MusicGalore.biz has offices in Los...Ch. 4 - Building Inspectors A city apportions 34 building...Ch. 4 - Prob. 9RECh. 4 - Prob. 10RECh. 4 - Corporate Security The Huntington-Hill...Ch. 4 - Essay Contest Four finalists are competing in an...Ch. 4 - Ski Club A campus ski club is trying o decide...Ch. 4 - Prob. 14RECh. 4 - Consumer Preferences A group of consumers were...Ch. 4 - Prob. 16RECh. 4 - Prob. 17RECh. 4 - Homecoming Queen Three high school students are...Ch. 4 - Prob. 19RECh. 4 - Prob. 20RECh. 4 - Prob. 21RECh. 4 - A weighted voting system for voters A. B. C. D....Ch. 4 - Prob. 23RECh. 4 - Prob. 24RECh. 4 - 25. Calculate the Banzhaf power indices for voters...Ch. 4 - Calculate the Banzhaf power indices for voters A,...Ch. 4 - Prob. 27RECh. 4 - Identify any dictator and all dummies for each...Ch. 4 - Four voters. A. B. C. and D. make decisions by...Ch. 4 - Postal Service The table below shows the number of...Ch. 4 - Computer Allocation The following table shows the...Ch. 4 - High School Counselors The following table shows...Ch. 4 - Prob. 4TCh. 4 - Consumer Preference One hundred consumers ranked...Ch. 4 - Prob. 6TCh. 4 - Exam Review A professor is preparing an extra...Ch. 4 - Prob. 8TCh. 4 - Drama Department The four staff members. A, B,C,...Ch. 4 - Three voters. A. B. and C, make decisions by using...
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