10-5 Exponential Functions
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1 10-5 Exponential Functions This presentation was created following the Fair Use Guidelines for Educational Multimedia. Certain materials are included under the Fair Use exemption of the U. S. Copyright Law. Further use of these materials and this presentation is restricted.
2 Objectives Students will graph exponential functions. Students will identify data that displays exponential behavior. 3/11/2008 2
3 Exponential Function An exponential function is a function that can be described by an equation of the form y = a x, where a>0 and a 1. 3/11/2008 3
4 Graph x x State the y-intercept. y Graph the ordered pairs and connect the points with a smooth curve. Answer: The y-intercept is 1. 3/11/2008 4
5 Use the graph to determine the approximate value of The graph represents all real values of x and their corresponding values of y for Answer: The value of y is about 5 when Use a calculator to confirm this value. 3/11/2008 5
6 a. Graph State the y-intercept. Answer: The y-intercept is 1. b. Use the graph to determine the approximate value of Answer: about 1.5 3/11/2008 6
7 Graph x 1 0 y 4 1 State the y-intercept. Graph the ordered pairs and connect the points with a smooth curve. 1 Answer: The y-intercept is 1. 3/11/2008 7
8 Use the graph to determine the approximate value of Answer: The value of y is about 8 when Use a calculator to confirm this value. 3/11/2008 8
9 a. Graph State the y-intercept. Answer: The y-intercept is 1. b. Use the graph to determine the approximate value of Answer: about 3 3/11/2008 9
10 Depreciation People joke that the value of a new car decreases as soon as it is driven off the dealer s lot. The function 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. 3/11/
11 Use a graphing calculator to graph the function. Answer: Only the values of V 25,000 and t 0 are meaningful in the context of the problem. 3/11/
12 What is the value of the car after one year? Original equation Use a calculator. Answer: After one year, the car s value is about $20,500. 3/11/
13 What is the value of the car after five years? Original equation Use a calculator. Answer: After five years, the car s value is about $ /11/
14 Depreciation The function 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. a. Graph the function. What values of V and t are meaningful in the function. Answer: Only the values of V 22,000 and t 0 are meaningful in the context of the problem. 3/11/
15 b. What is the value of the car after one year? Answer: $18,040 c. What is the value of the car after three years? Answer: $12,130 3/11/
16 Determine whether the set of data displays exponential behavior. x y Method 1 Look for a Pattern The domain values are at regular intervals of 10. Look for a common factor among the range values /11/
17 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. 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. 3/11/
18 Determine whether the set of data displays exponential behavior. x y Method 1 Look for a Pattern The domain values are at regular intervals of 10. The range values have a common difference of /11/
19 Answer: Since the domain values are at regular intervals and there is a common difference of 15, the data display linear behavior. Method 2 Graph the Data Answer: The graph is a line, not an exponential function. 3/11/
20 Determine whether the set of data displays exponential behavior. a. x y Answer: The domain values are at regular intervals and the range values have a common factor of so it is probably exponential. Also the graph shows rapidly decreasing values of y as x increases /11/
21 Determine whether the set of data displays exponential behavior. b. x y Answer: The domain values are at regular intervals and the range values have a common difference of 5. The data display linear behavior. 3/11/
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