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Over Lesson 7–4 What is 3,352,000 in scientific notation? What is 0.00000281 in scientific notation? What is 3 × 104 in standard form? What is 6.12 × 10–5 in standard form? Over Lesson 7–4 Answers 3.352 × 106 2.81 × 10–6 30,000 0.0000612 3 × 108 Exponential Functions Lesson 7-5 Understand how to graph exponential functions and to identify data that display exponential behavior. 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. 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 A. Graph y = 5x. B. Use the graph of y = 5x to determine the approximate value of 50.25. 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. 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. A. Graph 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 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 × 2.5 × 2.5 62.5 × 2.5 156.25 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. Determine whether the set of data displays exponential behavior. Homework Page 427 #11-39 odd, 26, 40, 51-67 odd