Lesson 5 Menu Five-Minute Check (over Lesson 9-4) Main Ideas and Vocabulary Targeted TEKS Key Concept: Exponential Function Example 1: Graph an Exponential.

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

Key Concept 9-5a

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

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

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

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

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

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

Lesson 5 CYP2 1.A 2.B 3.C 4.D A.about 1 B.about 3 C.about 2 D.about 0.1 B. Use the graph to determine the approximate value of

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

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

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

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

1.A 2.B 3.C 4.D Lesson 5 CYP3 A. Depreciation The function V = 22,000 ● 0.82 t models the depreciation of the value of a new car that originally cost $22,000. V represents the value of the car and t represents the time in years from the time the car was purchased. Graph the function. A.B. C.D.

1.A 2.B 3.C 4.D Lesson 5 CYP3 A.$21,000 B.$23,600 C.$18,040 D.$20,000 B. What is the value of the car after one year?

1.A 2.B 3.C 4.D Lesson 5 CYP3 A.$12,130 B.$25,120 C.$10,000 D.$15,000 C. What is the value of the car after three years?

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

Lesson 5 Ex4 Method 2Graph the Data Answer: The graph shows a rapidly increasing value of y as x increases. This is a characteristic of exponential behavior. 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.

1.A 2.B 3.C Lesson 5 CYP4 A.no B.yes C.cannot be determined Determine whether the set of data displays exponential behavior.