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Exponential Functions: Graphs and Problems

Learn how to graph exponential functions, identify exponential behavior, and use exponential functions to solve problems.

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Exponential Functions: Graphs and Problems

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  1. Five-Minute Check (over Lesson 9-4) Main Ideas and Vocabulary Targeted TEKS Key Concept: Exponential Function Example 1: Graph an Exponential Function with a > 1 Example 2: Graph an Exponential Function with 0 < a < 1 Example 3: Use Exponential Functions to Solve Problems Example 4: Identify Exponential Behavior Lesson 5 Menu

  2. Graph exponential functions. • Identify data that displays exponential behavior. • exponential function Lesson 5 MI/Vocab

  3. Key Concept 9-5a

  4. Graph an Exponential Function with a > 1 A. Graph y = 3x. State the y-intercept. Graph the ordered pairs and connect the points with a smooth curve. Answer: The y-intercept is 1. Lesson 5 Ex1

  5. Graph an Exponential Function with a > 1 B. Use the graph to determine the approximate value of 31.5. The graph represents all real values of x and their corresponding values of y for y = 3x. Answer: The value of y is about 5 when x = 1.5. Use a calculator to confirm this value. 31.5≈5.196 Lesson 5 Ex1

  6. A.B. C.D. A. Graph y = 5x. • A • B • C • D Lesson 5 CYP1

  7. B. Use the graph to determine the approximate value of 50.25. • A • B • C • D A. about 2.5 B. about 5 C. about 2 D. about 1.5 Lesson 5 CYP1

  8. A. Graph Exponential Functions with 0 < a < 1 Graph the ordered pairs and connect the points with a smooth curve. Answer: The y-intercept is 1. Lesson 5 Ex2

  9. B. Graph Exponential Functions with 0 < a < 1 Answer: The value of y is about 8 when x = –1.5. Use a calculator to confirm this value. Lesson 5 Ex2

  10. A. Graph State the y-intercept. A.B. C.D. • A • B • C • D Lesson 5 CYP2

  11. B. Use the graph to determinethe approximate value of • A • B • C • D A. about 1 B. about 3 C. about 2 D. about 0.1 Lesson 5 CYP2

  12. Use Exponential Functions to Solve Problems DEPRECIATION People joke that the value of a new car decreasesas soon as it is driven off the dealer’s lot. The function V = 25,000 ● 0.82t modelsthe depreciation of the value of a new car that originally cost $25,000. V represents thevalue of the car and t represents the time in years from the time thecar was purchased. Graph the function. What values of V and t are meaningful in thefunction? Use a graphing calculator to graph the function. Lesson 5 Ex3

  13. Use Exponential Functions to Solve Problems Answer: Only the values of 0 ≤V ≤ 25,000 and t≥ 0 are meaningful in the context of the problem. Lesson 5 Ex3

  14. Use Exponential Functions to Solve Problems B. What is the value of the car after one year? V = 25,000 ● 0.82t Original equation V = 25,000 ● 0.821 t = 1 V = 20,500 Use a calculator. Answer: After one year, the car's value is about $20,500. Lesson 5 Ex3

  15. Use Exponential Functions to Solve Problems C. What is the value of the car after five years? V = 25,000 ● 0.82t Original equation V = 25,000 ● 0.825 t = 5 V = 9268.50 Use a calculator. Answer: After five years, the car’s value is about $9270. Lesson 5 Ex3

  16. A.B. C.D. A. DepreciationThe function V = 22,000 ● 0.82t modelsthe depreciation of the value of a new car that originally cost $22,000. V represents thevalue of the car and t represents the time in years from the time thecar was purchased. Graph the function. • A • B • C • D Lesson 5 CYP3

  17. B. What is the value of the car after one year? • A • B • C • D A. $21,000 B. $23,600 C. $18,040 D. $20,000 Lesson 5 CYP3

  18. C. What is the value of the car after three years? • A • B • C • D A. $12,130 B. $25,120 C. $10,000 D. $15,000 Lesson 5 CYP3

  19. × 2.5 × 2.5 × 2.5 Identify Exponential Behavior Determine whether the set of data displays exponential behavior. Method 1 Look for a Pattern The domain values are at regular intervals of 10. Look for a common factor among the range values. 10 25 62.5 156.25 Lesson 5 Ex4

  20. Identify Exponential Behavior Answer: Since the domain values are at regular intervals and the range values have a common factor, the data are probably exponential. The equation for the data may involve (2.5)x. Method 2 Graph the Data Answer: The graph shows a rapidly increasing value of y as x increases. This is a characteristic of exponential behavior. Lesson 5 Ex4

  21. Determine whether the set of data displays exponential behavior. • A • B • C A. no B. yes C. cannot be determined Lesson 5 CYP4

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