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

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

3. 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

4. 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)

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

6. 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

7. Lesson 3: Graphs of Exponential Functions16 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)

8. 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

9. 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)

10. 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)

11. 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)

12. 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

13. 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

14. 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