1. Todays Lesson: Exponential Functions
February 22, 2016

2. Before we begin let’s do an activity!!! Paper folding
Take the provided sheet of paper.
Fold the paper in half once.
Open your paper back up. Trace the fold you created on your paper.
How many rectangles are now on your paper?
Record the data in the table below.

3. Continue
Using the same sheet of paper, repeat the process as many times as possible (fold the half in half again).
Record your answer in the table for each trial. Don’t forget to trace your new fold every time!

4. Folds and Rectangle Recording Sheet
Number of Folds
Number of Rectangles
Exponent Form 1 2 3 4 5 6 x
Exponential….

5. Table continue growth Number of Folds x Number of Rectangles y
Exponent Form 1 
2^0 1  2
 2^1 2  4
2^2 3  8
 2^3 4
 16
2^4 5
 32
 2^5 6
 64
 2^6
 2^x
Exponential….
growth 

6. Connections YES!! This is an example of an exponential
Is there a relationship between the number of folds and the number of rectangles?
y is the number of rectangles
x is the number of folds
YES!!
This is an example of an exponential
function. The input “x” is an exponent

7. Describe how the number rectangles changes as the number of folds increases.
2. Write an equation that describes the relationship between the number of folds and the number of rectangles.

8. 3. How many rectangles would there be if we could fold it 25 times
3. How many rectangles would there be if we could fold it 25 times? Explain how you know?
4- If your paper has 256 rectangles, how many times did you fold the paper?
5- Will there ever be a time when there are 0 rectangles on your paper? Explain.

10. Exit Ticket
What would you think will happen if we folded the paper in three every time instead of two…………

11. Exponential Functions
Exponential functions are in the form
𝑦= 𝒂 𝒃 𝑥
Where b > 0, and b ≠ 1, and x is any real number
Rate of change
Initial amount

12. Let’s Evaluate Exponential Functions
Recall: To evaluate means to _________________________________

13. More Practice Evaluating Exponentials
Evaluate the following (Round to the Nearest thousandths-3 decimals place)
𝑦= 5 𝑋 for x = -3
𝑦= ( 1 3 ) 𝑋 for x = 1 2
𝑦= 2 −𝑥 for x = 𝜋
.008
.577
.113

14. You may see exponential functions in this form
This time we have a number being multiplied by our exponential
We can evaluate these the same way

15. 𝑦=3 ● 5 𝑥 Evaluating Continued Evaluate the following When x = 1,2,& 3
X= 1 , y = _______
X = 2, y = ________
X = 3 , y = ________ 15 75
375

16. Let’s Graph Exponential Functions
Graph the following exponential functions.

17. Graph the following exponential functions.

18. Graphing Exponential Functions

21. Comparing the Graphs
What differences do you notice between the first two graphs and the second two graphs?

22. Extra Practice