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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.
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%
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.