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

• exponential function

• Graph exponential functions.

• Identify data that displays exponential behavior.

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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.

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

A. A

B. B

C. C

D. D

A B C D

0% 0%0%0%

A. Graph y = 5x.

A. B.

C. D.

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

B. Use the graph to determine the approximate value of 50.25.

A. about 2.5

B. about 5

C. about 2

D. about 1.5

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.

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

A B C D

0% 0%0%0%

A. Graph State the y-intercept.

A. B.

C. D.

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. about 1

B. about 3

C. about 2

D. about 0.1

B. Use the graph to determine

the approximate value of

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 ● 0.82t 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

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

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.

Use Exponential Functions to Solve Problems

Answer: After one year, the car's value is about $20,500.

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.

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

0%0%0%0%

A B C D

A. Depreciation The function V = 22,000 ● 0.82t 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

0%0%0%0%

A B C D

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

0%0%0%0%

A B C D

A. $12,130

B. $25,120

C. $10,000

D. $15,000

C. What is the value of the car after three years?

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

Identify Exponential Behavior

× 2.5 × 2.5 × 2.5

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.

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

0%0%0%

A B C

A. no

B. yes

C. cannot be determined

Determine whether the set of data displays exponential behavior.