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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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