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

Answers 3.352 × 106 2.81 × 10–6 30,000 0.0000612 3 × 108 5-Minute Check 2

Exponential Functions Lesson 7-5 Splash Screen

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

VOCABULARY Vocabulary

Concept

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

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

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

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

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

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

A. Graph Example 2

Example 2

Concept

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

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. 10 25 62.5 156.25 × 2.5 × 2.5 × 2.5 Example 4

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

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

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