1. What is 3,352,000 in scientific notation?
What is 3 × 104 in standard form?
What is 6.12 × 10–5 in standard form?
5-Minute Check 1

2. Answers
3.352 × 106
2.81 × 10–6
30,000
3 × 108
5-Minute Check 2

3. Exponential Functions
Lesson 7-5
Splash Screen

4. LEARNING GOAL
Understand how to use multiplication and division properties of exponents with rational exponents and how to multiply and divide numbers written in scientific notation.
Then/Now

5. VOCABULARY
Vocabulary

6. Concept

7. A. Graph y = 4x. Find the y-intercept and state the domain and range.
Graph with a > 0 and b > 1
A. Graph y = 4x. Find the y-intercept and state the domain and range.
Graph the ordered pairs and connect the points with a smooth curve.
Answer: The graph crosses the y-axis at 1, so the y-intercept is 1. The domain is all real numbers and the range is all positive real numbers.
Example 1

8. B. Use the graph of y = 4x to determine the approximate value of 41.5.
Graph with a > 0 and b > 1
B. Use the graph of y = 4x to determine the approximate value of 41.5.
The graph represents all real values of x and their corresponding values of y for y = 4x.
Answer: The value of y is 8 when x = 1.5.
Use a calculator to confirm this value.
41.5 = 8
Example 1

9. A. Graph y = 5x. x y -1 1 2 3
Example 1

10. B. Use the graph of y = 5x to determine the approximate value of 50.25.
Example 1

11. A. Find the y-intercept and state the domain and range.
Graph with a > 0 and 0 < b < 1
A Find the y-intercept and state the domain and range.
Graph the ordered pairs and connect the points with a smooth curve.
Answer: The y-intercept is 1. The domain is all real numbers and the range is all positive real numbers.
Example 2

12. Answer: The value of y is about 8 when x = –1.5.
Graph with a > 0 and 0 < b < 1
Answer: The value of y is about 8 when x = –1.5.
Use a calculator to confirm this value.
Example 2

13. A. Graph
Example 2

14. Example 2

15. Concept

16. B. DEPRECIATION The function V = 22,000 ● 0
B. 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. What is the value of the car after one year?
A. $21,000
B. $23,600
C. $18,040
D. $20,000
Example 3

17. Method 1 Look for a pattern.
Identify Exponential Behavior
Determine whether the set of data displays exponential behavior. Explain why or why not.
Method 1 Look for a pattern.
The domain values are at regular intervals of 10. Look for a common factor among the range values.
× 2.5
× 2.5
× 2.5
Example 4

18. Identify Exponential Behavior
Answer: Since the domain values are at regular intervals and the range values differ by a positive 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 rapidly increasing values of y as x increases. This is a characteristic of exponential behavior.
Example 4

19. Determine whether the set of data displays exponential behavior.
Example 4

20. Homework
p 427 #11-39 odd, 40
End of the Lesson