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Note Packet A Lesson 3: Graphs of Exponential Functions

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Lesson 3: Graphs of Exponential Functions Review : Graph the following story

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Darryl lives on the third floor of his apartment building which is 20 feet above the ground floor. His bike is locked up outside on the ground floor. At 3:00 p.m., he leaves to go run errands, but after he gets halfway down the stairs, he realizes he forgot his wallet. He goes back up the stairs to get it and then leaves again. As he tries to unlock his bike, he realizes that he forgot his keys. One last time, he goes back up the stairs to get his keys. He then unlocks his bike, and he is on his way at 3:10 p.m. What are some important pieces of information given in the story that will influence out sketch? Height – 20 feet Time – 10 min Movement At apartment (20 ft) Goes ½ way down (10ft) Goes back up Goes all the way down Goes all the way up Goes all the way down again

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Lesson 3: Graphs of Exponential Functions Height – 20 feet Time – 10 min Movement At apartment (20 ft) Goes ½ way down (10ft) Goes back up Goes all the way down Goes all the way up Goes all the way down again Now let’s graph it 2 4 6 8 10 12 14 Elevation (ft) 16 18 20 12345678910 Time (min) It probably takes him longer to go back up He probably spends at least a minute inside He walks to his bike but forgot the key Now connect the plotted points

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Lesson 3: Graphs of Exponential Functions What type of function is this? piecewise linear

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Lesson 3: Graphs of Exponential Functions Now let’s watch another videovideo We are going to sketch a graph to represent the bacteria growth, but let’s start by trying to count bacteria in order to fill out the table What is next? 163264128 Now let’s graph it

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Lesson 3: Graphs of Exponential Functions 163264128 123 Time (sec) 456 10 20 30 40 50 60 70 Number of Bacteria 80 90 100 This is called an exponential graph Unlike a quadratic graph, it does not make a U It would just keep going

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Lesson 3: Graphs of Exponential Functions Will the graph ever be vertical? Why or why not? No. It will continue to double, but time will always continue to go forward Since every second of video equals 20 minutes, how much real time in hours does our table and graph represent? 6 seconds 20 minutes= 120 minutes 120 minutes÷ 60 minutes= 2 hours

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Practice: Assume that a bacteria population doubles every hour. Which of the following three tables of data, with representing time in hours and the count of bacteria, could represent the bacteria population with respect to time? For all three tables of data, plot the graph of that data. Label the axes appropriately with units Time (hrs)Number of Bacteria 4 8 12 16 20 It cannot be this one. It is a linear graph and the numbers do not double

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Practice: Assume that a bacteria population doubles every hour. Which of the following three tables of data, with representing time in hours and the count of bacteria, could represent the bacteria population with respect to time? For all three tables of data, plot the graph of that data. Label the axes appropriately with units Time (hrs)Number of Bacteria 10 20 30 40 50 It could be this one. It is exponential and it doubles every time

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Practice: Assume that a bacteria population doubles every hour. Which of the following three tables of data, with representing time in hours and the count of bacteria, could represent the bacteria population with respect to time? For all three tables of data, plot the graph of that data. Label the axes appropriately with units Time (hrs)Number of Bacteria 10 20 30 40 50 This one is exponential BUT it doesn’t doubles every time So the answer is graph B

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Recap: The three types of graphs (linear, quadratic, and exponential) we have looked at over the past few days are the "pictures" of the main types of equations and functions we will be studying throughout this year. One of our main goals for the year is to be able to recognize linear, quadratic, and exponential relationships in real-life situations and develop a solid understanding of these functions to model those real-life situations. Sketch an example of all three of these types of graphs below

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Lesson 3: Graphs of Exponential Functions What is the difference between the quadratic graph and the exponential graph? A quadratic graph is shaped like a U An exponential graph has a curve on one side, but does not go up on the other side

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Lesson 3: Graphs of Exponential Functions Closing : Definition of Exponential Function A curved graph where the function starts slowly then increases/decreases at a much faster rate

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