MATHEMATICAL EXCURSIONS>LL<
4th Edition
ISBN: 9780357097977
Author: Aufmann
Publisher: CENGAGE LEARNING (CUSTOM)
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Question
Chapter 1.1, Problem 52ES
To determine
(a)
Find a counterexample to prove that the inductive argument in exercise
To determine
(b)
Find the counterexample of the statement is as follows.
The following equations show that
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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
they fake the data? At least for some hours (until the measurements would work again)? He used to spend a
lot of time online and thus knew the value of fake data, especially when it spread fast!
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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 1 Solutions
MATHEMATICAL EXCURSIONS>LL<
Ch. 1.1 - EXCURSION EXERCISES Solve each of the, following...Ch. 1.1 - EXCURSION EXERCISES Solve each of the, following...Ch. 1.1 - EXCURSION EXERCISES Solve each of the, following...Ch. 1.1 - EXCURSION EXERCISES Solve each of the, following...Ch. 1.1 - EXCURSION EXERCISES Solve each of the, following...Ch. 1.1 - EXCURSION EXERCISES Solve each of the, following...Ch. 1.1 - Use inductive reasoning to predict the next number...Ch. 1.1 - Use inductive reasoning to predict the next number...Ch. 1.1 - Use inductive reasoning to predict the next number...Ch. 1.1 - Use inductive reasoning to predict the next number...
Ch. 1.1 - Use inductive reasoning to predict the next number...Ch. 1.1 - Use inductive reasoning to predict the next number...Ch. 1.1 - Use inductive reasoning to predict the next number...Ch. 1.1 - Use inductive reasoning to predict the next number...Ch. 1.1 - Use inductive reasoning to predict the next number...Ch. 1.1 - Use inductive reasoning to predict the next number...Ch. 1.1 - Use inductive reasoning to decide whether each...Ch. 1.1 - Use inductive reasoning to decide whether each...Ch. 1.1 - Use inductive reasoning to decide whether each...Ch. 1.1 - Use inductive reasoning to decide whether each...Ch. 1.1 - Use inductive reasoning to decide whether each...Ch. 1.1 - Use inductive reasoning to decide whether each...Ch. 1.1 - Determine the distance a ball rolls, on inclined...Ch. 1.1 - Determine the distance a ball rolls, on inclined...Ch. 1.1 - For inclined plane 1, the distance a ball rolls in...Ch. 1.1 - For inclined plane 2, the distance a ball rolls in...Ch. 1.1 - Use inductive reasoning and the data in the...Ch. 1.1 - Use inductive reasoning and the data in the...Ch. 1.1 - Use inductive reasoning and the data in the...Ch. 1.1 - Use inductive reasoning and the data in the...Ch. 1.1 - Determine whether the argument is an example of...Ch. 1.1 - Determine whether the argument is an example of...Ch. 1.1 - Determine whether the argument is an example of...Ch. 1.1 - Determine whether the argument is an example of...Ch. 1.1 - Determine whether the argument is an example of...Ch. 1.1 - Determine whether the argument is an example of...Ch. 1.1 - Determine whether the argument is an example of...Ch. 1.1 - Determine whether the argument is an example of...Ch. 1.1 - Find a number that provides a counterexample to...Ch. 1.1 - Find a number that provides a counterexample to...Ch. 1.1 - Find a number that provides a counterexample to...Ch. 1.1 - Find a number that provides a counterexample to...Ch. 1.1 - Find a number that provides a counterexample to...Ch. 1.1 - Find a number that provides a counterexample to...Ch. 1.1 - Find a pair of numbers that provides a...Ch. 1.1 - Find a pair of numbers that provides a...Ch. 1.1 - Use deductive reasoning to determine the missing...Ch. 1.1 - Use deductive reasoning to determine the missing...Ch. 1.1 - Use deductive reasoning to show that the following...Ch. 1.1 - Use deductive reasoning to show that the following...Ch. 1.1 - Stocks Each of four siblings (Anita, Tony, Maria...Ch. 1.1 - Gourmet Chefs The Changs, Steinbergs, Ontkeans,...Ch. 1.1 - Collectibles The cities of Atlanta, Chicago,...Ch. 1.1 - Prob. 48ESCh. 1.1 - Driving Time You need to buy groceries at the...Ch. 1.1 - Driving Time Suppose, that you need to go to the...Ch. 1.1 - Use inductive reasoning to predict the next letter...Ch. 1.1 - Prob. 52ESCh. 1.1 - Counterexamples Find a counterexample to prove...Ch. 1.1 - Prob. 54ESCh. 1.2 - Extend Figure 1.1 above by constructing drawings...Ch. 1.2 - The figure below shows that the fourth triangular...Ch. 1.2 - Construct a drawing of the fourth hexagonal...Ch. 1.2 - Construct a difference table to predict the next...Ch. 1.2 - Construct a difference table to predict the next...Ch. 1.2 - Construct a difference table to predict the next...Ch. 1.2 - Construct a difference table to predict the next...Ch. 1.2 - Construct a difference table to predict the next...Ch. 1.2 - Construct a difference table to predict the next...Ch. 1.2 - Use the given nth-term formula to compute the...Ch. 1.2 - Use the given nth-term formula to compute the...Ch. 1.2 - Use the given nth-term formula to compute the...Ch. 1.2 - Use the given nth-term formula to compute the...Ch. 1.2 - Determine the nth-term formula for the number of...Ch. 1.2 - Determine the nth-term formula for the number of...Ch. 1.2 - Determine the nth-term formula for the number of...Ch. 1.2 - Determine the nth-term formula for the number of...Ch. 1.2 - Cannonballs can be stacked to form a pyramid with...Ch. 1.2 - Cannonballs can be stacked to form a pyramid with...Ch. 1.2 - Pieces vs. Cuts One cut of a stick of licorice...Ch. 1.2 - Pieces vs. Cuts One straight cut across a pizza...Ch. 1.2 - Pieces vs. Cuts One straight cut through a thick...Ch. 1.2 - Fibonacci Properties The Fibonacci sequence has...Ch. 1.2 - Find the third, fourth, and fifth terms of the...Ch. 1.2 - Find the third, fourth, and fifth terms of the...Ch. 1.2 - Binets Formula The following formula is known as...Ch. 1.2 - Binets Formula Simplified Binets formula (see...Ch. 1.2 - A Geometric Model The ancient Greeks often...Ch. 1.2 - The nth-term formula an=n(n1)(n2)(n3)(n4)4321+2n...Ch. 1.2 - Fibonacci Sums Make a conjecture for each of the...Ch. 1.2 - Fibonacci Sums Make a conjecture for each of the...Ch. 1.2 - Pascals Triangle The triangular pattern in the...Ch. 1.2 - A Savings Plan You save a penny on day 1. On each...Ch. 1.2 - A Famous Puzzle The Tower of Hanoi is a puzzle...Ch. 1.2 - Use the recursive definition for Fibonacci numbers...Ch. 1.3 - Use the probability demonstrator, in the left...Ch. 1.3 - Use the probability demonstrator, in the left...Ch. 1.3 - Use the probability demonstrator, in the left...Ch. 1.3 - Use the probability demonstrator, in the left...Ch. 1.3 - Use the probability demonstrator, in the left...Ch. 1.3 - Use Polyas four-step problem-solving strategy and...Ch. 1.3 - Use Polyas four-step problem-solving strategy and...Ch. 1.3 - Use Polyas four-step problem-solving strategy and...Ch. 1.3 - Use Polyas four-step problem-solving strategy and...Ch. 1.3 - Use Polyas four-step problem-solving strategy and...Ch. 1.3 - Use Polyas four-step problem-solving strategy and...Ch. 1.3 - Use Polyas four-step problem-solving strategy and...Ch. 1.3 - Use Polyas four-step problem-solving strategy and...Ch. 1.3 - Use Polyas four-step problem-solving strategy and...Ch. 1.3 - Use Polyas four-step problem-solving strategy and...Ch. 1.3 - Use Polyas four-step problem-solving strategy and...Ch. 1.3 - Use Polyas four-step problem-solving strategy and...Ch. 1.3 - Use Polyas four-step problem-solving strategy and...Ch. 1.3 - Use Polyas four-step problem-solving strategy and...Ch. 1.3 - Use Polyas four-step problem-solving strategy and...Ch. 1.3 - Use Polyas four-step problem-solving strategy and...Ch. 1.3 - Determine the Units Digit Determine the units...Ch. 1.3 - Determine the Units Digit Determine the units...Ch. 1.3 - Determine the Units Digit Determine the units...Ch. 1.3 - Determine the Units Digit Determine the units...Ch. 1.3 - Find Sums Find the following sums without using a...Ch. 1.3 - Explain how you could modify the procedure used by...Ch. 1.3 - Palindromic Numbers A palindromic number is a...Ch. 1.3 - Speed of a Car A car has an odometer reading of...Ch. 1.3 - A Puzzle Three volumes of the series Mathematics:...Ch. 1.3 - Connect the Dots Nine dots are arranged as shown....Ch. 1.3 - Movie Theatre Admissions The following bar graph...Ch. 1.3 - Box Office Revenues The following broken-line...Ch. 1.3 - Movie Ratings and Box Office Revenue The following...Ch. 1.3 - Votes in an Election In a school election one...Ch. 1.3 - Floor Design A square floor is tiled with...Ch. 1.3 - Number of Children How many children are there in...Ch. 1.3 - Brothers and Sisters I have two more sisters than...Ch. 1.3 - A Coin Problem If you take 22 pennies from a pile...Ch. 1.3 - Bacterial Growth The bacteria in a petri dish grow...Ch. 1.3 - Number of River Crossings Four people on one side...Ch. 1.3 - Examination Scores On three examinations, Dana...Ch. 1.3 - Puzzle from a Movie In the movie Die Hard: With a...Ch. 1.3 - Find the Fake Coin You have eight coins. They all...Ch. 1.3 - Problems from the Mensa Workout Mensa is a society...Ch. 1.3 - Problems from the Mensa Workout Mensa is a society...Ch. 1.3 - Problems from the Mensa Workout Mensa is a society...Ch. 1.3 - Problems from the Mensa Workout Mensa is a society...Ch. 1.3 - Compare Exponential Expressions a. How many times...Ch. 1.3 - A Famous Puzzle The mathematician Augustus De...Ch. 1.3 - Verify a Procedure Select a two-digit number...Ch. 1.3 - Numbering Pages How many digits does it take in...Ch. 1.3 - Mini Sudoku Sudoku is deductive reasoning...Ch. 1.3 - The Four 4s Problem The object at this exercise is...Ch. 1.3 - A Cryptarithm The following puzzle is a famous...Ch. 1 - Determine whether the argument is an example of...Ch. 1 - Determine whether the argument is an example of...Ch. 1 - Determine whether the argument is an example of...Ch. 1 - Determine whether the argument is an example of...Ch. 1 - Find a counterexample to show that the following...Ch. 1 - Find a counterexample to show that the following...Ch. 1 - Find a counterexample to show that the following...Ch. 1 - Find a counterexample to show that the following...Ch. 1 - Use a difference table to predict the next term of...Ch. 1 - Use a difference table to predict the next term of...Ch. 1 - A sequence has an nth-term formula of an=4n2n2....Ch. 1 - The first six terms of the Fibonacci sequence are:...Ch. 1 - Determine the nth-term formula for the number of...Ch. 1 - Determine the nth-term formula for the number of...Ch. 1 - Determine the nth-term formula for the number of...Ch. 1 - Determine the nth-term formula for the number of...Ch. 1 - Polyas Problem-Solving Strategy Solve each problem...Ch. 1 - Polyas Problem-Solving Strategy Solve each problem...Ch. 1 - Polyas Problem-Solving Strategy Solve each problem...Ch. 1 - Polyas Problem-Solving Strategy Solve each problem...Ch. 1 - Polyas Problem-Solving Strategy Solve each problem...Ch. 1 - Polyas Problem-Solving Strategy Solve each problem...Ch. 1 - Strategies List five strategies that are included...Ch. 1 - Strategies List three strategies that are included...Ch. 1 - Match Students with Their Major Michael, Clarissa,...Ch. 1 - Little League Baseball Each of the Little League...Ch. 1 - Prob. 27RECh. 1 - Find a Route The following map shows the 10...Ch. 1 - Areas of Rectangles Two perpendicular line segment...Ch. 1 - Use a Pattern in Make Predictions Consider the...Ch. 1 - A Cryptarithm In the following addition problem,...Ch. 1 - Make Change In how many different ways can change...Ch. 1 - Counting Problem In how many different orders can...Ch. 1 - Prob. 34RECh. 1 - Prob. 35RECh. 1 - Verify a Conjecture Use deductive reasoning to...Ch. 1 - Explain why 2004 nickels are worth more than 100.Ch. 1 - Gasoline Prices The following bar graph shows the...Ch. 1 - Super Bowl Ad Price The following graph shows the...Ch. 1 - Search Engine Rankings The following circle graph...Ch. 1 - Palindromic Numbers Recall that palindromic...Ch. 1 - Narcissistic Number A narcissistic number is a two...Ch. 1 - Number of Intersections Two different lines can...Ch. 1 - Prob. 44RECh. 1 - A Numerical Pattern A student has noticed the...Ch. 1 - Inductive vs. Deductive Reasoning Determine...Ch. 1 - Inductive vs. Deductive Reasoning Determine...Ch. 1 - Use a difference table to predict the next term in...Ch. 1 - List the first 10 terms of the Fibonacci sequence.Ch. 1 - In each of the following, determine the nth-term...Ch. 1 - A sequence has an nth-term formula of...Ch. 1 - Terms of a Sequence In a sequence: a1=3,a2=7 and...Ch. 1 - Number of Diagonal A diagonal of a polygon is a...Ch. 1 - State the four steps of Polyas four-step...Ch. 1 - Prob. 10TCh. 1 - Counting Problem In how many different ways can a...Ch. 1 - Units Digit What is the units digit (ones digit)...Ch. 1 - Vacation Money Shelly has saved same money for a...Ch. 1 - Number of Different Routes How many different...Ch. 1 - Number of League Games In a league of nine...Ch. 1 - Ages of Children The four children in the Rivera...Ch. 1 - Counterexample Find a counterexample to show that...Ch. 1 - Counterexample Find a counterexample to show that...Ch. 1 - Find a Sum Find the following sum without using a...Ch. 1 - Motor Vehicle Thefts The following graph shows the...
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