 ## CCSS.MATH.CONTENT.HSF.LE.A.2

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### In this episode of Algebra Applications, students explore earthquakes using exponential models. In particular, students analyze the earthquake that struck the Sichuan Province in China in 2008, months before the Beijing Olympics. This dramatic, real-world example allows students to apply their understanding of exponential functions and their inverses, along with data analysis and periodic function analysis. This video includes a Video Transcript: https://www.media4math.com/library/video-transcript-algebra-applications-exponential-functions ### In this introductory segment students learn about the great earthquake of 2008 that hit the Sichuan province of China. In the process they learn about how exponential functions provide a good model for describing earthquake intensity. To see the video transcript for this video, click here: https://www.media4math.com/library/video-transcript-algebra-applications-exponential-functions-segment-1-introduction ### The basic definition of an exponential function is shown in the intensity function for an earthquake. Students analyze data and perform an exponential regression based on data from the Sichuan earthquake. This video includes a video transcript: https://www.media4math.com/library/video-transcript-algebra-applications-exponential-functions-segment-2-what-earthquake A Promethean Flipchart is available for this video: https://www.media4math.com/library/promethean-flipchart-algebra-applications-earthquakes-1 ### An exponential model describes the intensity of an earthquake, while a logarithmic model describes the magnitude of an earthquake. In the process students learn about the inverse of an exponential function.  This video includes a video transcript: https://www.media4math.com/library/video-transcript-algebra-applications-exponential-functions-segment-3-what-difference A Promethean Flipchart is available for this video: https://www.media4math.com/library/promethean-flipchart-algebra-applications-earthquakes-2 ### An earthquake is an example of a seismic wave. A wave can be modeled with a trigonometric function. Using the TI-Nspire, students link the amplitude to an exponential function to analyze the dramatic increase in intensity resulting from minor changes to magnitude. This video includes a video transcript: https://www.media4math.com/library/video-transcript-algebra-applications-exponential-functions-segment-4-how-earthquake A Promethean Flipchart is available for this video: https://www.media4math.com/library/promethean-flipchart-algebra-applications-earthquakes-3 ### Almost everyone has an intuitive understanding that exponential growth means rapid growth. Written and hosted by internationally acclaimed math educator Dr. Monica Neagoy, this video builds on students’ intuitive notions, explores exponential notation, and analyzes properties of exponential function graphs, with the help of TI-Nspire features such as sliders and graph transformations. Using exponential functions to model finance applications and a Newton’s law of cooling problem further help students build a solid foundation for these fundamental algebraic concepts. Concepts explored: functions, exponents, exponential functions. This video includes a Video Transcript: https://www.media4math.com/library/video-transcript-algebra-nspirations-exponents-and-exponential-functions A Promethean Flipchart is available for this video: https://www.media4math.com/library/promethean-flipchart-algebra-nspirations-exponential-functions ### In this Investigation we explore the properties of exponents and exponential graphs. This video is Segment 1 of a 4 segment series related to Exponents and Exponential Functions. Segments 1 and 2 are grouped together. To access Exponents and Exponential Functions, Segment 2, click the following link: • https://www.media4math.com/library/algebra-nspirations-exponents-and-exponential-functions-segment-2 A Video Transcript for Exponents and Exponential Functions, Segments 1 and 2 is available via the following link: • https://www.media4math.com/library/video-transcript-algebra-nspirations-exponents-and-exponential-functions-part-1 ### In this Math Lab students compare the graphs of quadratics and exponential graph of base 2. This video is Segment 1 of a 4 segment series related to Exponents and Exponential Functions. Segments 1 and 2 are grouped together. To access Exponents and Exponential Functions, Segment 1, click the following link: • https://www.media4math.com/library/algebra-nspirations-exponents-and-exponential-functions-segment-1 A Video Transcript for Exponents and Exponential Functions, Segments 1 and 2 is available via the following link: • https://www.media4math.com/library/video-transcript-algebra-nspirations-exponents-and-exponential-functions-part-1 ### In this Investigation we look at exponential growth and decay models. This video is Segment 3 of a 4 segment series related to Exponents and Exponential Functions. Segments 3 and 4 are grouped together. To access Exponents and Exponential Functions, Segment 4, click the following link: • https://www.media4math.com/library/algebra-nspirations-exponents-and-exponential-functions-segment-4 A Video Transcript for Exponents and Exponential Functions, Segments 3 and 4 is available via the following link: • https://www.media4math.com/library/video-transcript-algebra-nspirations-exponents-and-exponential-functions-part-2 ### In this Math Lab we look at cooling curves. This video is Segment 4 of a 4 segment series related to Exponents and Exponential Functions. Segments 3 and 4 are grouped together. To access Exponents and Exponential Functions, Segment 3, click the following link: • https://www.media4math.com/library/algebra-nspirations-exponents-and-exponential-functions-segment-3 A Video Transcript for Exponents and Exponential Functions, Segments 3 and 4 is available via the following link: • https://www.media4math.com/library/video-transcript-algebra-nspirations-exponents-and-exponential-functions-part-2 ### The definition of the term "Graphs of Exponential Functions." ### In this Slide Show, use the Desmos graphing calculator to explore exponential functions. Note: The download is a PPT file. ### In this Slide Show, use the Desmos graphing calculator to explore logarithmic functions. Note: The download is a PPT file. ### INSTRUCTIONAL RESOURCE: Exponential Functions ### Example 1: The graph of an exponential function of the form y = a * b^(cx), under the following conditions: 0 < b < 1, a = 1, c = 1. ### Example 2: The graph of an exponential function of the form y = a * b^(cx), under the following conditions: 0 < b < 1, a = 1, c > 1. ### Example 3: The graph of an exponential function of the form y = a * b^(cx), under the following conditions: 0 < b < 1, a = 1, c < 0. ### Example 4: The graph of an exponential function of the form y = a * b^(cx), under the following conditions: 0 < b < 1, a = 1, 0< c < 1. ### Example 5: The graph of an exponential function of the form y = a * b^(cx), under the following conditions: 0 < b < 1, a > 0, c = 1. ### Example 6: The graph of an exponential function of the form y = a * b^(cx), under the following conditions: 0 < b < 1, a < 0, c = 1. ### Example 7: The graph of an exponential function of the form y = a * b^(cx), under the following conditions: 0 < b < 1, a > 0, c > 1. ### Example 8: The graph of an exponential function of the form y = a * b^(cx), under the following conditions: 0 < b < 1, a < 0, c > 1. ### Example 9: The graph of an exponential function of the form y = a * b^(cx), under the following conditions: 0 < b < 1, a > 0, 0 < c < 1. ### Example 10: The graph of an exponential function of the form y = a * b^(cx), under the following conditions: 0 < b < 1, 0 < c < 1. ### Example 11: The graph of an exponential function of the form y = a * b^(cx), under the following conditions: b = 2, a = 1, c = 1. 