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Advanced Algebra II Notes 1.3 A First Look at Limits

Advanced Algebra II Notes 1.3 A First Look at Limits. Limit: the mathematical value toward which a function goes as the independent variable approaches infinity (long term value). Coffee cooling Tree growing World record high jump. Part I:.

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Advanced Algebra II Notes 1.3 A First Look at Limits

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  1. Advanced Algebra II Notes 1.3 A First Look at Limits • Limit: the mathematical value toward which a function goes as the independent variable approaches infinity (long term value). • Coffee cooling • Tree growing • World record high jump

  2. Part I: Our kidneys continuously filter our blood, removing impurities. In this investigation you will simulate what happens in the body when a patient takes medicine. To represent the blood in a patient’s body, use a bowl containing a total of 1 liter (L) of liquid. Start with 16 milliliters (mL) of tinted liquid to represent a dose of medicine in the blood, and use clear water for the rest. • 16 mL of medicine (colored water) and 984 mL of pure blood (pure water). • The kidney filters out 25% of the medicine each day. Fresh water (representing filtered blood) replaces the medicine removed. Complete the table of the amount of medicine in the body each day.

  3. Doses of Medicine 12 9 6.75

  4. Recursive formula for the daily amount of medicine in the body: ___________________ • Number of days before there is less than 1 mL of medicine in the blood? _______ • Is the medicine ever completely removed from the blood? Why/why not? __________ • ______________________________________________________________________ • Sketch a graph of the data: 10 no There will always be a trace of medicine

  5. Part II • Doctors sometimes prescribe regular doses of medicine. This time the patient will take regular doses daily over a period of time. • 16 mL of medicine and 984 mL of pure blood. • Each day, 250 mL is removed and replaced with 234 mL of blood (water) and 16 mL of medicine (colored water)

  6. 16 28 37 43.75

  7. Complete the Table • Write a recursive formula that generates this sequence. _________________________ • Does the blood every turn into pure medicine? Why/why not? • ____________________ • ___________________________________________________________________ • Sketch a graph to represent the data and label it. No, pure water is always added at each step

  8. Example • Antonio and Deanna are working at the community pool for the summer. They need to provide a “shock” treatment of 450 g of dry chlorine to prevent the growth of algae in the pool, then they add 45 g of chlorine each day after the initial treatment. Each day, the sun burns off 15% of the chlorine. Find the amount of chlorine after 1 day, 2 days, and 3 days. Create a graph of the data.

  9. Assignment: page 48: 1, 3 - 12

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