# Lesson 3: Graphs of Exponential Functions

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Lesson 3: Graphs of Exponential Functions
Note Packet A Lesson 3: Graphs of Exponential Functions

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

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

Lesson 3: Graphs of Exponential Functions
Now let’s graph it 20 Height – 20 feet 18 Time – 10 min 16 Movement At apartment (20 ft) 14 Goes ½ way down (10ft) 12 Goes back up It probably takes him longer to go back up 10 Elevation (ft) 8 He probably spends at least a minute inside 6 Goes all the way down 4 He walks to his bike but forgot the key 2 Goes all the way up Goes all the way down again 1 2 3 4 5 6 7 8 9 10 Now connect the plotted points Time (min)

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

Lesson 3: Graphs of Exponential Functions
Now let’s watch another video 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? 16 32 64 128 Now let’s graph it

Lesson 3: Graphs of Exponential Functions
16 32 64 128 100 This is called an exponential graph 90 80 Unlike a quadratic graph, it does not make a U 70 60 Number of Bacteria 50 It would just keep going 40 30 20 10 1 2 3 4 5 6 Time (sec)

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

Practice: Assume that a bacteria population doubles every hour
Practice: Assume that a bacteria population doubles every hour. Which of the following three tables of data, with 𝑥 representing time in hours and 𝑦 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 20 It cannot be this one. It is a linear graph and the numbers do not double 16 Number of Bacteria 12 8 4 Time (hrs)

It could be this one. It is exponential and it doubles every time
Practice: Assume that a bacteria population doubles every hour. Which of the following three tables of data, with 𝑥 representing time in hours and 𝑦 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 50 It could be this one. It is exponential and it doubles every time 40 Number of Bacteria 30 20 10 Time (hrs)

This one is exponential BUT it doesn’t doubles every time
Practice: Assume that a bacteria population doubles every hour. Which of the following three tables of data, with 𝑥 representing time in hours and 𝑦 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 This one is exponential BUT it doesn’t doubles every time 50 40 Number of Bacteria 30 20 So the answer is graph B 10 Time (hrs)

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

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

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