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# 8.2 Notes Half-Life, Compounding Continuously

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### 8.2 Notes Half-Life, Compounding Continuously

1. 1. 8.2 Properties of Exponential Functions
2. 2. <ul><li>Example 1. </li></ul><ul><li>The half-life of a radioactive substance is the time it takes for half of the material to decay. A hospital prepares a 100-mg supply of technetium-99m, which has a half-life of 6 hours. </li></ul><ul><li>Make a table showing the amount </li></ul>The half-life of a radioactive substance is the time it takes for half of the material to decay. A hospital prepares a 100-mg supply of technetium-99m, which has a half-life of 6 hours. a. Make a table showing the amount of technetium-99m that remains at the end of each 6-hour interval for 36 hours. b. Write an exponential function to find the amount of technetium-99m that remains after 75 hours.
3. 3. Technetium-99m (mg) Number of hours elapsed 6 5 4 3 2 1 0 Number of 6-hour intervals
4. 4. Example 2. Arsenic-7 is used to locate brain tumors and has a half-life of 17.5 days. Write an exponential decay function for a 90-mg sample. Use the function to find the amount remaining after 6 days.
5. 5. What is e?
6. 6. Compounding Interest Continuously <ul><li>A = Pe rt </li></ul>
7. 7. Example 3 . Suppose you invest \$1050 in an account that pays an annual interest rate of 5.5% compounded continuously. How much will you have in the account after 5 years?
8. 8. <ul><li>Assignment: </li></ul><ul><li>Pg. 434 #15 – 17, 24 – 26, 30, 37, 40 </li></ul>