splash screen. then/now you evaluated numerical expressions involving exponents. graph exponential...
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You evaluated numerical expressions involving exponents.
• Graph exponential functions.
• Identify data that display exponential behavior.
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• exponential function
• exponential growth function
• exponential decay function
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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.
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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 ofx 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
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A. Graph y = 5x.
A. B.
C. D.
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B. Use the graph of y = 5x to determine the approximate value of 50.25.
A. about 2.5
B. about 5
C. about 2
D. about 1.5
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Graph with a > 0 and 0 < b < 1
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.
A. Find the y-intercept and state
the domain and range.
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Graph with a > 0 and 0 < b < 1
Use a calculator to confirm this value.
Answer: The value of y is about 8 when x = –1.5.
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A. Graph
A. B.
C. D.
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A. about 1
B. about 3
C. about 2
D. about 0.1
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Use Exponential Functions to Solve Problems
A. DEPRECIATION Some people say 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.
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Use Exponential Functions to Solve Problems
Answer: Only the values of 0 ≤ V ≤ 25,000 and t ≥ 0 are meaningful in the context of the problem.
Since t represents time, t > 0. At t = 0, the value of the car is $25,000, so V ≤ 25,000.
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Use Exponential Functions to Solve Problems
B. 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 Use a calculator.
Answer: After five years, the car's value is about $9268.
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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.
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A. $21,000
B. $23,600
C. $18,040
D. $20,000
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?
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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
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Identify Exponential Behavior
Method 2 Graph the data.
Answer: The graph shows rapidly increasing values of y as x increases. This is a characteristic of 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.
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A. no
B. yes
C. cannot be determined
Determine whether the set of data displays exponential behavior.
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