Alg 1 TE Lesson 10-8

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PowerPoint Additional Examples 2 Which kind of data best models the data below? Write an equation to model the data. a. x y 0 0 1 1.4 2 5.6 3 12.6 4 22.4 b. quadratic; y ≠ 1.4x 2 x -1 4 0 2 1 1 exponential; y ≠ 2 ? 0.5 x 3 Suppose you are studying deer that live in an area. The data below were collected by a local conservation organization. It indicates the number of deer estimated to be living in the area over a five-year period. Determine which kind of function best models the data. Write an equation to model the data. exponential; y ≠ 90 ? 0.77 x Resources • Daily Notetaking Guide 10-8 L3 • Daily Notetaking Guide 10-8— Adapted Instruction L1 Closure y 2 0.5 3 0.25 Estimated Year Population 0 90 1 69 2 52 3 40 4 31 Real-World Quick Check Connection Frog populations around the world have been declining over the past 20 years. 2 3 Which kind of function best models the data in each table? Write an equation to model the data. a. x y b. x y c. x y 0 4 1 0 0 0 2 1 4.4 1 1 1 0.5 2 4.84 1 2 2 2 1 2 3 5.324 3 4.5 3 2 4 5.8564 4 8 exponential; y ≠ 4 ? 1.1 x 1 1 linear; y ≠ x ± quadratic; y ≠– 1 x 2 2 2 2 While real-world data seldom fall exactly into linear, exponential, or quadratic patterns, you can find a best-possible model. EXAMPLE Real-World Problem Solving Zoology Suppose you are studying frogs that live in a nearby wetland area. The data at the right were collected by a local conservation organization. They indicate the number of frogs estimated to be living in the wetland area over a five-year period. Determine which kind of function best models the data. Write an equation to model the data. Step 1 Graph the data to decide which model is most appropriate. Population Step 2 Test for a common ratio. 1 1 1 1 120 80 40 0 1 2 3 4 5 6 Year Year 0 1 2 3 4 Estimated Population 120 101 86 72 60 The graph curves, and it does not look quadratic. It may be exponential. The population of frogs is roughly 0.84 times its value the previous year. Step 3 Write an exponential model. Relate y = a ? b x Define Let a = the initial value, 120. Let b = the decay factor, 0.84. Write y = 120 ? 0.84 x 101 120 0.84 86 101 0.85 72 86 0.84 60 72 0.83 Year 0 1 2 3 4 The common ratio is roughly 0.84. Estimated Population 120 101 86 72 60 Ask students how to choose a linear, quadratic, or exponential model for data. First graph the data to see if the graph is linear or if it curves. Then look for a best fit model. 600 Chapter 10 Quadratic Equations and Functions 600
Quick Check EXERCISES Practice and Problem Solving A GO Practice by Example for Help Example 1 (page 597) Step 4 Test two points other than (0, 120). y = 120 ? 0.84 3 y = 120 ? 0.84 4 y < 71 y < 60 The point (3, 71) is close to the data point (3, 72). The predicted value (4, 60) matches the corresponding data point. The equation y = 120 ? 0.84 x models the data. Year Profit (dollars) 3 The profits of a small company are shown 0 0 in the table at the right. Let x = 0 correspond 1 5,000 to the year 2000. 2 20,000 a. Determine which kind of function best models the data. quadratic 3 44,000 b. Write an equation to model the data. y ≠ 5000x 2 4 79,000 For more exercises, see Extra Skill and Word Problem Practice. 1–6. See Graph each set of points. Which model is most appropriate for each set? back of book. 1. (-2, -3), (-1, 0), (0, 1), (1, 0), (2, -3) 2. (-2, -8), (0, -4), (3, 2), (5, 6) 3. (-3, 6), (-1, 0), (0, -1), (1, -1.5) 4. (-2, 5), (-1, -1), (0, -3), (1, -1), (2, 5) 5. Q-2, 25 8 , -1, 25 2 9 R Q 3 R, (0, -5), (2, 3) 6. (-3, 8), (-1, 6), (0, 5), (2, 3), (3, 2) 3. Practice Assignment Guide 1 A B 1-27 C Challenge 28-29 Test Prep 30-33 Mixed Review 34-48 Homework Quick Check To check students’ understanding of key skills and concepts, go over Exercises 8, 14, 17, 18, 20. Error Prevention! Exercises 1–6 Be sure students do not quickly determine that the best model is exponential as soon as they see that the graph is not linear. They need to graph all points to see if the graph is a quadratic model. Example 2 (page 599) Example 3 (page 600) Which kind of function best models the data in each table? Write an equation to model the data. 7. x y 8. x y 9. x y 0 0 0 5 0 0 1 1.5 1 3 1 2.8 2 6 2 1 2 11.2 3 13.5 3 1 3 25.2 4 24 4 3 4 44.8 quadratic; y ≠ 1.5x 2 linear; y ≠ 2x – 5 quadratic; y ≠ 2.8x 2 10. x y 11. x y 12. x y 0 1 1 1.2 2 1.44 3 1.728 0 5 1 2 2 0.8 3 0.32 4 2.0736 4 0.128 4 0 exponential; y ≠ 1 ? 1.2 x exponential; y ≠ 5 ? 0.4 x 1 linear; y ≠– 2 x ± 2 13. The table at the right shows the end-of-themonth balance in a checking account. Month Balance (dollars) a. Graph the data. Does the graph suggest a linear, exponential, or quadratic model? 1 2 58 123 b. Find the differences of consecutive terms. 3 187 Are they roughly the same? 65, 64, 64; yes c. Estimate a common difference based on 4 251 your answer to part (b). 64 d. Write an equation to model the data. y ≠ 64x – 5 a. See back of book. 0 2 1 1.5 2 1 3 0.5 Lesson 10-8 Choosing a Linear, Quadratic, or Exponential Model 601 GPS Enrichment Guided Problem Solving Reteaching Adapted Practice Practice © Pearson Education, Inc. All rights reserved. Name Class Date Practice 10-9 Choosing a Linear, Quadratic, or Exponential Model Which kind of function best models the data? Write an equation to model the data. 1. (-1, 3), (1, 3), (3, 27), (5, 75), (7, 147) 2. (-2, 4), (-1, 2), (0, 0), (1, -2), (2, -4) 3. ¢ 22, ≤, ¢ 21, 1 ≤, (0, 1), (1, 4), (2, 16) 4. (-6, -1), (-3, 0), (0, 1), (3, 2), (6, 3) 16 1 4 5. ¢ 22, 1 3 ≤,(-1, 1), (0, 3), (1, 9), (2, 27) 6. (-4, -32), (-2, -8), (0, 0), (2, -8), (4, -32) 7. 8. 9. x y x y -3 9 2 -2 2 1 -1 2 0 0 10. 11. 12. x y x y 0 -2 1 -8 2 -32 3 -128 13. ¢ 22, ≤, ¢ 21, ≤, ¢ 0, 1 ≤, ¢ 1, 1 ≤, ¢ 2, 1 ≤ 3 1 1 3 3 3 3 14. ¢ 21, 2 1 ≤, ¢ 0, 2 1 ≤, (1, -1), (2, -2), (3, -4) 4 2 15. The cost of shipping computers from a warehouse is given in the table below. Number of Computers 50 75 100 125 Cost (dollars) 1700 2500 3300 4100 a. Determine which kind of function best models the data. b. Write an equation to model the data. -1 -2 0 -4 1 -6 2 -8 -7 -245 -5 -125 -3 -45 -1 -5 c. On the basis of your equation, what is the cost of shipping 27 computers? d. On the basis of your equation, how many computers could be shipped for $5500? 16. During a scientific experiment, the bacteria count was taken at 5-min intervals. The data shows the count at several time periods during the experiment. Time Interval 0 1 2 3 Count 110 132 159 190 a. Determine which kind of function best models the data. b. Write an equation to model the data. c. On the basis of your equation, what is the count 1 hr, 45 min after the start of the experiment? x y -4 -4 -2 -1 x -2 0 0 2 -1 0 y 3 2 1 2 1 2 - 2 4 - 2 3 L4 L1 L3 L2 L3 601
Page 1 and 2: 10-8 What You’ll Learn • To cho
Page 3: x y 1 20 0 8 1 3.2 2 1.28 3 0.512 2
Page 7 and 8: 25b. The second common difference i

Alg 1 TE Lesson 10-8

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