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DO NOW. HW: Exponential Functions Worksheet Warm-Up: What is the formula for compound interest? What is different about the formula for exponential decay?. Exponential Functions Review Jeopardy. Linear, Quad., or Exp. Growth & Decay 2. Analyze the Equation. Growth & Decay.

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  1. DO NOW • HW: Exponential Functions Worksheet • Warm-Up: What is the formula for compound interest? What is different about the formula for exponential decay?

  2. Exponential Functions Review Jeopardy

  3. Linear, Quad., or Exp. Growth & Decay 2 Analyze the Equation Growth & Decay Geometric Sequences 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 5 5 5 5 5

  4. Analyze for 1 Question: Does the following equation represent growth or decay y = 100(1.06)x Check Your Answer

  5. Analyze for 1 Answer: Back to the Game Board

  6. Analyze for 2 Question: What is the starting amount in the equation below? y = 2450(.86)x Check Your Answer

  7. 2450 Analyze for 2 Answer: Back to the Game Board

  8. Analyze for 3 Question: Identify the initial amount and the growth factor: y = 250(1.065)x Check Your Answer

  9. Analyze for 3 Answer: Initial amount: 250 Growth factor: 1.065 Back to the Game Board

  10. Analyze for 4 Question: What is the percent growth? y = 5(1.02)x Check Your Answer

  11. Analyze for 4 Answer: Back to the Game Board

  12. Analyze for 5 Question: The equation below represents the value of Caleb’s savings account. y = 500(1+ (.08/12))12(16) • How much money did he start with? • What is the percent interest he earns? • How often is it compounded? • How many years is it compounded for? Check Your Answer

  13. Analyze for 5 Answer: • How much money did he start with? $500 • What is the percent interest he earns? 8% • How often is it compounded? monthly • How many years is it compounded for? 16 Back to the Game Board

  14. Growth & Decay for 1 Question: A $25000 purchase decreases 12% in value each year. Determine the value of the purchase after 7 years using the equation y = 25000(.88)xAbsolute Value Check Your Answer

  15. $10,216.89 Growth & Decay for 1 Answer: Back to the Game Board

  16. Growth & Decay for 2 Question: A town with a population of 5,000 grows 3% each year. Find the population at the end of 10 years. Check Your Answer

  17. y = 5000(1.03)10 6,720 (rounded) Growth & Decay for 2 Answer: Back to the Game Board

  18. Growth & Decay for 3 Question: Carbon-14 has a half-life of 5,700 years. Suppose the average page of a book containing approximately 8 mg is put into a time capsule. How much carbon-14 will each page contain after 22,800 years? Write the equation and give your answer. Check Your Answer

  19. Growth & Decay for 3 Answer: y = 8(.5)4 .5 mg Back to the Game Board

  20. Growth & Decay for4 Question: A piece of equipment costs $75,000 new but depreciates 12% per year in each succeeding year. Find its value after 8 years. Check Your Answer

  21. Growth & Decay for4 Answer: y = 75000(1 - .12)8 $26972.59 Back to the Game Board

  22. Growth & Decay for5 Question: Find the value of $1000 deposited for 8 years in an account paying 8% annual interest compounded semiannually. Check Your Answer

  23. Growth & Decay for5 Answer: y = 1000 (1 + (.08/2))2(8) $1872.98 Back to the Game Board Check Your Answer

  24. Growth & Decay for 1 Question: There are 5,000 fish in the pond and the population is increasing by 2.1% each year. Using the equation y = 5000(1.021)x, how many fish will there be after 15 years? Back to the Game Board Check Your Answer

  25. Growth & Decay for1 Answer: 6829 fish (rounded) Back to the Game Board

  26. Growth & Decay for2 Question: Write an exponential function to model the situation. Then estimate the value of the function after 5 years (to the nearest whole number). A population of 290 animals that increases at an annual rate of 9%. Check Your Answer

  27. Growth & Decay for2 Answer: y = 290(1 + .09)5 446 animals Back to the Game Board

  28. Growth & Decay for3 Question: The population of fish in the pond (with no predators) doubles every day. If the pond started with 5 fish, how many would there be after 8 days if the pattern continues. Check Your Answer

  29. Growth & Decay for3 Answer: y = 5(2)8 1280 fish Back to the Game Board

  30. Growth & Decay for4 Question: Write an exponential function to model the situation. Then estimate the value of the function after 5 years (to the nearest whole number). A population of 220 animals that decreases at an annual rate of 19%. Check Your Answer

  31. Growth & Decay for4 Answer: y = 220(1 - .19)5 77 animals Back to the Game Board

  32. Growth & Decay for5 Question: Find the value of $1000 deposited for 10 years in an account paying 6% annual interest compounded monthly. Check Your Answer

  33. Growth & Decay for5 Answer: y = 1000 (1 + (.06/12))12(10) $1819.40 Back to the Game Board

  34. Linear, Quad., Exp for 1 Question: Check Your Answer

  35. Linear, Quad., Exp for 1 Answer: linear Back to the Game Board

  36. Linear, Quad., Exp for 2 Question: y = 7x2 +5x – 2 WHY? Check Your Answer

  37. Linear, Quad., Exp for 2 Answer: Quadratic Has an x squared Back to the Game Board

  38. Linear, Quad., Exp for 3 Question: WHY? Check Your Answer

  39. Linear, Quad., Exp for 3 Answer: Exponential – multiplies by ¼ each time Back to the Game Board

  40. Linear, Quad., Exp for 4 Question: The table shows the body temperature of a desert spiny lizard at various air temperatures. Write the equation that fits the best Check Your Answer

  41. Linear, Quad., Exp for 4 Answer: Linear y = .34x + 24.6 Back to the Game Board

  42. Linear, Quad., Exp for 5 Question: The time it takes for a clock’s pendulum to swing from one side to another and back again is called the pendulums period. The table shows the period of a pendulum of length l. Write the equation that best fits the data. Round to the nearest hundredth. Check Your Answer

  43. Linear, Quad., Exp for 5 Answer: Quadratic is best y=.8x2 + .09x - .09 Back to the Game Board

  44. Geometric Sequences for 1 Question: Find the next three terms of the sequence: 4, 12, 36, 108… Check Your Answer

  45. Geometric Sequences for 1 Answer: 540, 1620, 4860 Back to the Game Board

  46. Geometric Sequences for 2 Question: What is the common ratio in the sequence: 2, -8, 32, -128 Check Your Answer

  47. Geometric Sequences for 2 Answer: r = -4 Back to the Game Board

  48. Geometric Sequences for 3 Question: What is the common ratio in the sequence: -100, -40, -16, -6.4 Check Your Answer

  49. Geometric Sequences for 3 Answer: .4 or 2/5 Back to the Game Board

  50. Geometric Sequences for 4 Question: Is the following sequence geometric? -0.2, -0.02, -0.002, -0.0002 Check Your Answer

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