To determine The amount of Radium -226 that will be left after 1000 years and 10000 years if the half-life of Radium -226 metal is 1600 years and one starts with 1 kilogram of radium -226. Explanation Given: The amount of Radium -226 is exponentially decaying and it has a half-life of 1600 years with initial population 1 kilogram. Formula used: As the quantity is exponentially decaying, the amount at time t must take the form N ( t ) = N ( 0 ) 2 − ( t t h a l f ) Calculation: t h a l f = 1600 years

Using & Understanding Mathematics: A Quantitative Reasoning Approach (7th Edition)

7th Edition

ISBN: 9780134715919

Author: Bennett

Publisher: PEARSON

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Chapter 8.B, Problem 48E

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The amount of Radium-226 that will be left after 1000years and 10000 years if the half-life of Radium-226 metal is 1600 years and one starts with 1 kilogram of radium-226.

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Chapter 8.B, Problem 47E

Chapter 8.B, Problem 49E

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5. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.AE.003. y y= ex² 0 Video Example x EXAMPLE 3 (a) Use the Midpoint Rule with n = 10 to approximate the integral कर L'ex² dx. (b) Give an upper bound for the error involved in this approximation. SOLUTION 8+2 1 L'ex² d (a) Since a = 0, b = 1, and n = 10, the Midpoint Rule gives the following. (Round your answer to six decimal places.) dx Ax[f(0.05) + f(0.15) + ... + f(0.85) + f(0.95)] 0.1 [0.0025 +0.0225 + + e0.0625 + 0.1225 e0.3025 + e0.4225 + e0.2025 + + e0.5625 €0.7225 +0.9025] The figure illustrates this approximation. (b) Since f(x) = ex², we have f'(x) = 0 ≤ f'(x) = < 6e. ASK YOUR TEACHER and f'(x) = Also, since 0 ≤ x ≤ 1 we have x² ≤ and so Taking K = 6e, a = 0, b = 1, and n = 10 in the error estimate, we see that an upper bound for the error is as follows. (Round your final answer to five decimal places.) 6e(1)3 e 24( = ≈

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Chapter 8 Solutions

Using & Understanding Mathematics: A Quantitative Reasoning Approach (7th Edition)

Ch. 8.A - A town’s population increases in one year from...Ch. 8.A - A town’s population increases in one year from...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 - Decide whether each of the following statements...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 - Linear or Exponential? State whether the growth...Ch. 8.A - Prob. 10E Ch. 8.A - Linear or Exponential? State whether the growth...Ch. 8.A - Prob. 12E Ch. 8.A - Linear or Exponential? State whether the growth...Ch. 8.A - Linear or Exponential? State whether the growth...Ch. 8.A - Linear or Exponential? State whether the growth...Ch. 8.A - 9-16: Linear or Exponential? State whether the...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 - Chessboard Parable. Use the chessboard parable...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 - 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 - Suppose your salary increases at a rate of 4.5%...Ch. 8.B - Which of the following is not a good approximation...Ch. 8.B - A town’s population doubles in 23 years. Its...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 - The population of an endangered species decreases...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 - 23-24. Logarithm Calculations 24. Using the...Ch. 8.B - Doubling Time. Each exercise gives a doubling time...Ch. 8.B - Doubling Time. Each exercise gives a doubling time...Ch. 8.B - Doubling Time. Each exercise gives a doubling time...Ch. 8.B - 25-32: Doubling Time. Each exercise gives a...Ch. 8.B - Doubling Time. Each exercise gives a doubling time...Ch. 8.B - Doubling Time. Each exercise gives a doubling time...Ch. 8.B - Doubling Time. Each exercise gives a doubling time...Ch. 8.B - 25-32: Doubling Time. Each exercise gives a...Ch. 8.B - World Population. In 2017, estimated world...Ch. 8.B - World Population. In 2017, estimated world...Ch. 8.B - 31. Rabbits. A community of rabbits begins with an...Ch. 8.B - Prob. 36E Ch. 8.B - Approximate Doubling Time Formula. Use the...Ch. 8.B - 37-40: Approximate Doubling Time Formula. Use the...Ch. 8.B - Approximate Doubling Time Formula. Use the...Ch. 8.B - 37-40: Approximate Doubling Time Formula. Use the...Ch. 8.B - Half-Life. Each exercise gives a half-life for an...Ch. 8.B - Half-Life. Each exercise gives a half-life for an...Ch. 8.B - Half-Life. Each exercise gives a half-life for an...Ch. 8.B - 41 -48: Half-Life. Each exercise gives a half-life...Ch. 8.B - 41-48: Half-Life. Each exercise gives a half-life...Ch. 8.B - 41 -48: Half-Life. Each exercise gives a half-life...Ch. 8.B - 41-48: Half-Life. Each exercise gives a half-life...Ch. 8.B - 41 -48: Half-Life. Each exercise gives a half-life...Ch. 8.B - Approximate Half-Life Formula. Use the approximate...Ch. 8.B - 49-52: Half-Life Formula. Use the approximate...Ch. 8.B - Approximate Half-Life Formula. Use the approximate...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 - Exact Formulas. Compare the doubling times found...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 - Prob. 59E 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 - 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 - World population is currently rising by about 80...Ch. 8.C - The most recent doubling of world population took...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 - 12. Past civilizations that no longer exist must...Ch. 8.C - Varying Growth Rates. Starting from a 2017 world...Ch. 8.C - Varying Growth Rates. Starting from a 2017 world...Ch. 8.C - Varying Growth Rates. Starting from a 2017 world...Ch. 8.C - Varying Growth Rates. Starting from a 2017 world...Ch. 8.C - Birth and Death Rates. The following table gives...Ch. 8.C - 17-20: Birth and Death Rates. The following table...Ch. 8.C - 17-20: Birth and Death Rates. The following table...Ch. 8.C - Birth and Death Rates. The following table gives...Ch. 8.C - 21. Logistic Growth. Consider a population that...Ch. 8.C - Logistic Growth. Consider a population that begins...Ch. 8.C - U.S Population. Starting from an estimated U.S....Ch. 8.C - Prob. 24E Ch. 8.C - Prob. 25E Ch. 8.C - Prob. 26E Ch. 8.C - Prob. 27E Ch. 8.C - 28. Slower Growth. Repeat Exercise 27, but use a...Ch. 8.C - Prob. 29E Ch. 8.C - World Carrying Capacity. For the given carrying...Ch. 8.C - 29-32: World Carrying Capacity. For the given...Ch. 8.C - 29-32: World Carrying Capacity. For the given...Ch. 8.C - Prob. 33E Ch. 8.C - Prob. 34 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.C - Prob. 40E Ch. 8.D - Prob. 1QQ Ch. 8.D - Prob. 2QQ Ch. 8.D - 3. What is a 0-decibel sound? the softest sound...Ch. 8.D - 4. A sound of 85 decibels is defined to be a. 85...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? 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Use the decibel scale to answer...Ch. 8.D - Prob. 20E Ch. 8.D - Prob. 21E Ch. 8.D - Prob. 22E Ch. 8.D - Prob. 23E Ch. 8.D - Inverse Square Law. Use the inverse square law for...Ch. 8.D - 25-32: The pH Scale. Use the pH scale to answer...Ch. 8.D - 25-32: The pH Scale. Use the pH scale to answer...Ch. 8.D - 25-32: The pH Scale. Use the pH scale to answer...Ch. 8.D - Prob. 28E Ch. 8.D - Prob. 29E Ch. 8.D - Prob. 30E Ch. 8.D - Prob. 31E Ch. 8.D - Prob. 32E 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 - Prob. 42E Ch. 8.D - Earthquakes in the News. Find a recent news story...Ch. 8.D - Disasters. Find the death lolls for some of the...Ch. 8.D - Prob. 45E Ch. 8.D - Prob. 46E Ch. 8.D - Ocean Acidification. Research ocean acidification...

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