Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)

6th Edition

ISBN: 9780321914620

Author: Jeffrey O. Bennett, William L. Briggs

Publisher: PEARSON

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Textbook Question

Chapter 8.A, Problem 23E

Magic Penny Parable. Use the magic penny parable presented in the text.

How much money would you have after 22 days?
Suppose that you stacked the pennies alter 22 days. How high would the suck rise, in kilometers? (Him: Find a few pennies and a ruler.)
How many days would elapse before you had a total of more than $1 billion? (Hint: Proceed by trial and error.)
Suppose that you could keep making a single stack of the pennies. Alter how many days would the stack be long enough io reach the nearest star (beyond the Sun), which is about 4.3 light-years (4.0 ×10^l³km) away? (Him: Proceed by trial and error.)

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Chapter 8.A, Problem 22E

Chapter 8.A, Problem 24E

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7. [10 marks] Let G = (V,E) be a 3-connected graph. We prove that for every x, y, z Є V, there is a cycle in G on which x, y, and z all lie. (a) First prove that there are two internally disjoint xy-paths Po and P₁. (b) If z is on either Po or P₁, then combining Po and P₁ produces a cycle on which x, y, and z all lie. So assume that z is not on Po and not on P₁. Now prove that there are three paths Qo, Q1, and Q2 such that: ⚫each Qi starts at z; • each Qi ends at a vertex w; that is on Po or on P₁, where wo, w₁, and w₂ are distinct; the paths Qo, Q1, Q2 are disjoint from each other (except at the start vertex 2) and are disjoint from the paths Po and P₁ (except at the end vertices wo, W1, and w₂). (c) Use paths Po, P₁, Qo, Q1, and Q2 to prove that there is a cycle on which x, y, and z all lie. (To do this, notice that two of the w; must be on the same Pj.)

Chapter 8 Solutions

Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)

Ch. 8.A - Prob. 1QQ Ch. 8.A - Prob. 2QQ Ch. 8.A - The balance owed your credit card doubles from...Ch. 8.A - The number Of songs in your iPod has increased...Ch. 8.A - Which of the following is in example of...Ch. 8.A - On a chessboard with 64 squares, you place 1 penny...Ch. 8.A - At 11:00 you place a single bacterium in a bottle,...Ch. 8.A - Consider the bacterial population described in...Ch. 8.A - Consider the bacterial population described in...Ch. 8.A - Which of the following is not true of any...

Ch. 8.A - Describe basic differences between linear growth...Ch. 8.A - 2. Briefly explain how repeated doublings...Ch. 8.A - Briefly summarize the Story Of the bacteria in the...Ch. 8.A - Explain the meaning Of the two key facts about...Ch. 8.A - Prob. 5E Ch. 8.A - Suppose you had a magic hank account in which your...Ch. 8.A - A small town that grows exponentially can become a...Ch. 8.A - H. Human population has been growing exponentially...Ch. 8.A - Prob. 9E Ch. 8.A - Prob. 10E Ch. 8.A - Prob. 11E Ch. 8.A - Prob. 12E Ch. 8.A - Prob. 13E Ch. 8.A - Prob. 14E Ch. 8.A - Linear or Exponential? State whether the growth...Ch. 8.A - Prob. 16E Ch. 8.A - Chessboard Parable. Use the chessboard parable...Ch. 8.A - Chessboard Parable. Use the chessboard parable...Ch. 8.A - Chessboard Parable. Use the chessboard parable...Ch. 8.A - Prob. 20E Ch. 8.A - Magic Penny Parable. Use the magic penny parable...Ch. 8.A - Prob. 22E Ch. 8.A - Magic Penny Parable. Use the magic penny parable...Ch. 8.A - Magic Penny Parable. Use the magic penny parable...Ch. 8.A - Bacteria in a Bottle Parable. Use the bacteria...Ch. 8.A - Bacteria in a Bottle Parable. Use the bacteria...Ch. 8.A - Bacteria in a Bottle Parable. Use the bacteria...Ch. 8.A - Bacteria in a Bottle Parable. Use the bacteria...Ch. 8.A - 29. Human Doubling. Human population in the year...Ch. 8.A - Doubling Time versus Initial Amount. a. Would you...Ch. 8.A - Facebook Users. The table shows the number of...Ch. 8.A - Prob. 32E Ch. 8.A - Exponential Growth. Identify at least two news...Ch. 8.A - Prob. 34E Ch. 8.A - Prob. 35E Ch. 8.B - Prob. 1QQ Ch. 8.B - Prob. 2QQ Ch. 8.B - Which of the following is not a good approximation...Ch. 8.B - Prob. 4QQ Ch. 8.B - Radioactive tritium (hvdrogen-3) has a halt-life...Ch. 8.B - Radioactive uramum-235 has a hall-life of about...Ch. 8.B - Prob. 7QQ Ch. 8.B - log10108= a.100,000,000 b. 108 c.8 Ch. 8.B - A rural popular ion decreases at a rate of 20% per...Ch. 8.B - Prob. 10QQ Ch. 8.B - What is a doubling tune? Suppose a population has...Ch. 8.B - Prob. 2E Ch. 8.B - State the approximate doubting time formula and...Ch. 8.B - Prob. 4E Ch. 8.B - Prob. 5E Ch. 8.B - 6. State the approximate hall-life formula and the...Ch. 8.B - 7. Briefly describe exact doubling time and...Ch. 8.B - 8. Give an example in which it is important to use...Ch. 8.B - Our town is growing with a doubling time of 25...Ch. 8.B - Our town is growing at a rate of 7% per year, so...Ch. 8.B - A toxic chemical decays with a hall-life of 10...Ch. 8.B - The hall-life of plutomum-239 is about 24,000...Ch. 8.B - Logarithms. Refer to the Brief Review on p. 488....Ch. 8.B - Logarithms. Refer to the Brief Review on p. 488....Ch. 8.B - Prob. 15E Ch. 8.B - Prob. 16E Ch. 8.B - 13-24: Logarithms. Refer to the Brief Review on p....Ch. 8.B - Prob. 18E Ch. 8.B - Logarithms. Refer to the Brief Review on p. 488....Ch. 8.B - Logarithms. Refer to the Brief Review on p. 488....Ch. 8.B - 13-24: Logarithms. Refer to the Brief Review on p....Ch. 8.B - Prob. 22E Ch. 8.B - Prob. 23E Ch. 8.B - Logarithms. Refer to the Brief Review on p. 488....Ch. 8.B - Prob. 25E Ch. 8.B - Prob. 26E Ch. 8.B - Prob. 27E Ch. 8.B - Prob. 28E Ch. 8.B - Prob. 29E Ch. 8.B - Prob. 30E Ch. 8.B - Prob. 31E Ch. 8.B - Prob. 32E Ch. 8.B - Prob. 33E Ch. 8.B - Prob. 34E Ch. 8.B - 31. Rabbits. A community of rabbits begins with an...Ch. 8.B - Prob. 36E Ch. 8.B - Doubling Time Formula. Use the approximate...Ch. 8.B - Prob. 38E Ch. 8.B - Prob. 39E Ch. 8.B - Prob. 40E Ch. 8.B - Prob. 41E Ch. 8.B - Prob. 42E Ch. 8.B - Prob. 43E Ch. 8.B - 41 -48: Half-Life. Each exercise gives a half-life...Ch. 8.B - Prob. 45E Ch. 8.B - 41 -48: Half-Life. Each exercise gives a half-life...Ch. 8.B - Prob. 47E Ch. 8.B - 41 -48: Half-Life. Each exercise gives a half-life...Ch. 8.B - Prob. 49E Ch. 8.B - 49-52: Half-Life Formula. Use the approximate...Ch. 8.B - Prob. 51E Ch. 8.B - 49-52: Half-Life Formula. Use the approximate...Ch. 8.B - Prob. 53E Ch. 8.B - Exact Formulas. Compare the doubling times found...Ch. 8.B - Prob. 55E Ch. 8.B - Exact Formulas. Compare the doubling times found...Ch. 8.B - Prob. 57E Ch. 8.B - 58. Nuclear Weapons. Thermonuclear weapons use...Ch. 8.B - Fossil Fuel Emissions. Total emissions of carbon...Ch. 8.B - Yucca Mountain. The U.S. government spent nearly...Ch. 8.B - Crime Rate. The homicide rate decreases at a rate...Ch. 8.B - 62. Drug Metabolism. A particular antibiotic is...Ch. 8.B - Atmospheric Pressure. The pressure of Earth's...Ch. 8.B - Prob. 64E Ch. 8.B - 65. Radioactive Half-Life. Find a news story that...Ch. 8.B - Prob. 66E Ch. 8.B - Prob. 67E Ch. 8.B - Prob. 68E Ch. 8.B - Prob. 69E Ch. 8.C - Prob. 1QQ Ch. 8.C - Prob. 2QQ Ch. 8.C - The primary reason for the rapid growth of human...Ch. 8.C - The carrying capacity of the Earth is defined as...Ch. 8.C - Which of the billowing would cause estimates of...Ch. 8.C - 6. Recall the bacteria in a bottle example from...Ch. 8.C - When researchers project that human population...Ch. 8.C - Prob. 8QQ Ch. 8.C - Prob. 9QQ Ch. 8.C - Prob. 10QQ Ch. 8.C - Based on Figure 8.3, contrast the changes in human...Ch. 8.C - Prob. 2E Ch. 8.C - Haw do today’s birth and death rates compare to...Ch. 8.C - Prob. 4E Ch. 8.C - Prob. 5E Ch. 8.C - What is overshot and collapse? Under what...Ch. 8.C - Prob. 7E Ch. 8.C - 8. If birth rates fall more than death rates, the...Ch. 8.C - The carrying capacity of our planet depends only...Ch. 8.C - to rapid increases in computing technology, we...Ch. 8.C - In the wild, we always expect the population of...Ch. 8.C - Prob. 12E Ch. 8.C - Prob. 13E Ch. 8.C - Varying Growth Rates. Starting from a 2013...Ch. 8.C - Prob. 15E Ch. 8.C - 13-16: Varying Growth Rates. Starting from a 2013...Ch. 8.C - Birth and Death Rates. The following table gives...Ch. 8.C - Prob. 18E Ch. 8.C - Prob. 19E Ch. 8.C - Prob. 20E Ch. 8.C - 21. Logistic Growth. Consider a population that...Ch. 8.C - Logistic Growth. Consider a population that begins...Ch. 8.C - Prob. 23E Ch. 8.C - Prob. 24E Ch. 8.C - Prob. 25E Ch. 8.C - Prob. 26E Ch. 8.C - Prob. 27E Ch. 8.C - Prob. 28E Ch. 8.C - Prob. 29E Ch. 8.C - Prob. 30E Ch. 8.C - Prob. 31E Ch. 8.C - Prob. 32E Ch. 8.C - Prob. 33E Ch. 8.C - Prob. 34.0E Ch. 8.C - Prob. 34.1E Ch. 8.C - Population Predictions. Find population...Ch. 8.C - Prob. 36E Ch. 8.C - Prob. 37E Ch. 8.C - Prob. 38E Ch. 8.C - Prob. 39E Ch. 8.D - The energy release of a magnitude 7 earthquake is...Ch. 8.D - Prob. 2QQ Ch. 8.D - 3. What is a 0-decibel sound? the softest sound...Ch. 8.D - Prob. 4QQ Ch. 8.D - Prob. 5QQ Ch. 8.D - Prob. 6QQ Ch. 8.D - Prob. 7QQ Ch. 8.D - Prob. 8QQ Ch. 8.D - Prob. 9QQ Ch. 8.D - Prob. 10QQ Ch. 8.D - What is the magnitude scale for earthquakes? What...Ch. 8.D - What is the decibel scale? Describe how it is...Ch. 8.D - What is pH? What pH values define an acid, a base,...Ch. 8.D - What is acid rain? Why is it a serious...Ch. 8.D - 5. An earthquake of magnitude 8 will do twice as...Ch. 8.D - A 120-dB wand is 20% louder than a 100-dB sound.Ch. 8.D - If I double the amount of water in the cup, I'll...Ch. 8.D - The lake water was crystal clear, so It could not...Ch. 8.D - Earthquake Magnitudes. Use the earthquake...Ch. 8.D - Prob. 10E Ch. 8.D - Prob. 11E Ch. 8.D - Earthquake Magnitudes. Use the earthquake...Ch. 8.D - Earthquake Magnitudes. Use the earthquake...Ch. 8.D - 9-14: Earthquake Magnitudes. Use the earthquake...Ch. 8.D - The Decibel Scale. Use the decibel scale to answer...Ch. 8.D - The Decibel Scale. Use the decibel scale to answer...Ch. 8.D - The Decibel Scale. Use the decibel scale to answer...Ch. 8.D - The Decibel Scale. Use the decibel scale to answer...Ch. 8.D - The Decibel Scale. Use the decibel scale to answer...Ch. 8.D - Prob. 20E Ch. 8.D - Inverse Square Law. Use the inverse square law for...Ch. 8.D - Prob. 22E Ch. 8.D - Inverse Square Law. Use the inverse square law for...Ch. 8.D - Inverse Square Law. Use the inverse square law for...Ch. 8.D - The pH scale. Use the pH scale to answer the...Ch. 8.D - The pH Scale. Use the pH scale to answer the...Ch. 8.D - Prob. 27E Ch. 8.D - Prob. 28E Ch. 8.D - Prob. 29E Ch. 8.D - Prob. 30E Ch. 8.D - The pH Scale. Use the pH scale to answer the...Ch. 8.D - 25-32: The pH Scale. Use the pH scale to answer...Ch. 8.D - Logarithmic Thinking. Briefly describe, in words,...Ch. 8.D - 33-38: Logarithmic Thinking. Briefly describe, in...Ch. 8.D - Logarithmic Thinking. Briefly describe, in words,...Ch. 8.D - Logarithmic Thinking. Briefly describe, in words,...Ch. 8.D - Prob. 37E Ch. 8.D - Prob. 38E Ch. 8.D - 39. Sound and Distance. The decibel level for...Ch. 8.D - 40. Variation in Sound with Distance. Suppose that...Ch. 8.D - Toxic Dumping in Acidified Lakes. Consider a...Ch. 8.D - Earthquakes in the News. Find a recent news story...Ch. 8.D - Prob. 43E Ch. 8.D - Disasters. Find the death lolls for some of the...Ch. 8.D - Prob. 45E

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