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Chapter 4 Review Exercises

Chapter 4 Review Exercises
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  • 15. Medicine

    Subjects in a study receive daily doses of a medicine for 10 weeks. In the first week, they receive 100 milligrams each day. Each week thereafter, the dosage decreases 10% from the previous week. Write a formula that represents the daily dosage during each week.

    • Worked-Out Solution

      The formula for this exponential decay is

      P = 100 people, r = 10%, n is the number of weeks

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     _____     _    _     ______    ______    _____   
    |  __ \\  | || | ||  /_   _//  /_   _//  / ____|| 
    | |  \ || | || | ||  `-| |,-    -| ||-  / //---`' 
    | |__/ || | \\_/ ||    | ||     _| ||_  \ \\___   
    |_____//   \____//     |_||    /_____//  \_____|| 
     -----`     `---`      `-`'    `-----`    `----`  
                                                      
    
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  • 16. Making a Table to Show Medicine Dosage

    Subjects in a study receive daily dose of a medicine for 10 weeks. In the first week, they receive 100 milligrams each day. Each week thereafter, the dosage decreases 10% from the previous week. Make a table showing the daily dosage during the 10 weeks.

    A spreadsheet is available to help you complete this exercise.

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      _____      ___     ______     _____     ______  
     |__  //    / _ \\  |      \\  |  ___||  /_____// 
       / //    / //\ \\ |  --  //  | ||__    `____ `  
      / //__  |  ___  |||  --  \\  | ||__    /___//   
     /_____|| |_||  |_|||______//  |_____||  `__ `    
     `-----`  `-`   `-` `------`   `-----`   /_//     
                                             `-`      
    
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  • 17. Graphing the Decrease of Medicine Dosage

    Subjects in a study receive daily doses of a medicine for 10 weeks. In the first week, they receive 100 milligrams each day. Each week thereafter, the dosage decreases 10% from the previous week. Sketch a graph showing the decrease in the daily dosage during the 10 weeks.

    A spreadsheet is available to help you complete this exercise.

    • Worked-Out Solution

      The formula for this exponential decay is

      P = 100 people, r = 10%, n is the number of weeks

       

      Use a spreadsheet to graph the dosage for the 10 weeks.

      data folder

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       _____   _    _    __   _     ______   _    _   
      / ___// | || | || | || | ||  /_   _// | || | || 
      \___ \\ | || | || | '--' ||   -| ||-  | || | || 
      /    // | \\_/ || | .--. ||   _| ||_  | \\_/ || 
     /____//   \____//  |_|| |_||  /_____//  \____//  
    `-----`     `---`   `-`  `-`   `-----`    `---`   
                                                      
    
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  • 18. Half-life of Medicine

    Subjects in a study receive daily doses of a medicine for 10 weeks. In the first week, they receive 100 milligrams each day. Each week thereafter, the dosage decreases 10% from the previous week. The half-life of the medicine is 24 hours. How much of the medicine received in a dose during week 10 remains in the patient's bloodstream after 24 hours?

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      ______     ___      ____     _    _     _  _   
     /_____//   / _ \\   |  _ \\  | || | ||  | \| || 
     `____ `   | / \ ||  | |_| || | || | ||  |  ' || 
     /___//    | \_/ ||  | .  //  | \\_/ ||  | .  || 
     `__ `      \___//   |_|\_\\   \____//   |_|\_|| 
     /_//       `---`    `-` --`    `---`    `-` -`  
     `-`                                             
    
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  • 19. Technetium

    Most technetium is man-made in nuclear reactors. There are many isotopes of technetium, two of which are technetium-99 and technetium-99m. The half-life of technetium-99 is 210,000 years. How much of a 120-gram sample of technetium-99 will remain after 630,000 years?

    • Worked-Out Solution

      After 210,000 years,

      remain. After another 210,000 years

      remain. After another 210,000 years

      remain. So, after 630,000 years, 15 grams remain.

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      _____      ___     _    _    __   __    _  __  
     / ____||   / _ \\  | || | ||  \ \\/ //  | |/ // 
    / //---`'  | / \ || | || | ||   \ ` //   | ' //  
    \ \\___    | \_/ || | \\_/ ||    | ||    | . \\  
     \_____||   \___//   \____//     |_||    |_|\_\\ 
      `----`    `---`     `---`      `-`'    `-` --` 
                                                     
    
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  • 20. Decay of Technetium

    Most technetium is man-made in nuclear reactors. There are many isotopes of technetium, two of which are technetium-99 and technetium-99m. The half-life of technetium-99 is 210,000 years. A vial contains 10 grams of technetium-99m. Use the spreadsheet to determine how long it will take the 10 grams of technetium-99m to decay to about 2.1 grams

    data folder

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      _____    __   __   _____     __   __   _    _   
     |__  //   \ \\/ // |  __ \\   \ \\/ // | \  / || 
       / //     \ ` //  | |  \ ||   \ ` //  |  \/  || 
      / //__     | ||   | |__/ ||    | ||   | .  . || 
     /_____||    |_||   |_____//     |_||   |_|\/|_|| 
     `-----`     `-`'    -----`      `-`'   `-`  `-`  
                                                      
    
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  • 21. Half-life of Technetium

    A vial contains 10 grams of technetium-99m. The table shows the amount remaining after various periods of time.

    What is the half-life of technetium-99m? Explain your reasoning.

    • Worked-Out Solution

      From the table, you can see that it took 6 years for the amount to decay from 10 grams to 5 grams.

      This implies that the half-life is 6 years.

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                ______   _    _    __   __   _    _   
      ____     /_   _// | || | ||  \ \\/ // | |  | || 
     |    \\    -| ||-  | || | ||   \ ` //  | |/\| || 
     | [] ||    _| ||_  | \\_/ ||    | ||   |  /\  || 
     |  __//   /_____//  \____//     |_||   |_// \_|| 
     |_|`-`    `-----`    `---`      `-`'   `-`   `-` 
     `-`                                              
    
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  • 22. Storing Technetium

    Most technetium is man-made in nuclear reactors. There are many isotopes of technetium, two of which are technetium-99 and technetium-99m. The half-life of technetium-99 is 210,000 years. A solution containing technetium-99m is often injected into a patient to help diagnose problems in the body. Explain why a hospital or veterinary clinic should not order excessive amounts of technetium-99m with the intent of placing it in storage.

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      ______     ___      _____     _____    _    _   
     /_   _//   / _ \\   |__  //   |  ___|| | |  | || 
     `-| |,-   / //\ \\    / //    | ||__   | |/\| || 
       | ||   |  ___  ||  / //__   | ||__   |  /\  || 
       |_||   |_||  |_|| /_____||  |_____|| |_// \_|| 
       `-`'   `-`   `-`  `-----`   `-----`  `-`   `-` 
                                                      
    
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