Some radioactive elements, such as Iodine-123 are used in medical imaging. Radioactive elements tend to decay exponentially, over time. Suppose I discovered a new radioactive element and in a moment of ego-crazed self-grandizement, decided to call it Pankownium-123. Suppose also, that my newly discovered element decays in such a way that 84% of the initial amount remains after each one-hour period. Part A: If you begin with 200mg of Pankownium, find the exponential equation that describes the amount remaining after x hours. The equation should be of the form y = a ∙ b t (do not use an equation calculated by Excel). Then create a two-column table for the amount remaining after each hour for hour numbers 0 – 19. Column 1 is the hour number and column 2 is the amount that remains. Use your graphing calculator to define your equation and to help you with table values. Please round remaining amounts of the element to the nearest tenth of a milligram. Part B: Using Excel, copy your table from part A into a spreadsheet and create a scatter plot, which correctly displays the values from this table. The hour number should be the x-axis variable and the amount of the element that remains should be the y-axis variable. Your spreadsheet should include each of the following items: - Your Name - The table, including the column titles - A descriptive and easily readable chart title - Descriptive and easy to read titles for both the x and y-axis - An exponential curve-of-best-fit - Answers to each of the questions below (round all mg amounts to the nearest tenth) 1. State the exponential equation you created in part A. 2. What is the percentage rate of decay each hour for the amount of this element? 3. How many milligrams of Pankownium remain after 4 hours? 4. How many milligrams remain after 19 hours? 5. At what hour number will the remaining amount fall below 1 milligram? 6. At what hour will the remaining amount fall below one-tenth of a milligram?

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Some radioactive elements, such as Iodine-123 are used in medical imaging. Radioactive elements tend to decay exponentially, over time. Suppose I discovered a new radioactive element and in a moment of ego-crazed self-grandizement, decided to call it Pankownium-123. Suppose also, that my newly discovered element decays in such a way that 84% of the initial amount remains after each one-hour period. Part A: If you begin with 200mg of Pankownium, find the exponential equation that describes the amount remaining after x hours. The equation should be of the form y = a ∙ b t (do not use an equation calculated by Excel). Then create a two-column table for the amount remaining after each hour for hour numbers 0 – 19. Column 1 is the hour number and column 2 is the amount that remains. Use your graphing calculator to define your equation and to help you with table values. Please round remaining amounts of the element to the nearest tenth of a milligram. Part B: Using Excel, copy your table from part A into a spreadsheet and create a scatter plot, which correctly displays the values from this table. The hour number should be the x-axis variable and the amount of the element that remains should be the y-axis variable. Your spreadsheet should include each of the following items: - Your Name - The table, including the column titles - A descriptive and easily readable chart title - Descriptive and easy to read titles for both the x and y-axis - An exponential curve-of-best-fit - Answers to each of the questions below (round all mg amounts to the nearest tenth) 1. State the exponential equation you created in part A. 2. What is the percentage rate of decay each hour for the amount of this element? 3. How many milligrams of Pankownium remain after 4 hours? 4. How many milligrams remain after 19 hours? 5. At what hour number will the remaining amount fall below 1 milligram? 6. At what hour will the remaining amount fall below one-tenth of a milligram?

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