1. Warm-up Identify the exponent & the base number.
1) 24 2) -3x4 3) -3●4x 4) (4x)2
5) Which of the above represents an exponential expression?

2. 3.1 Exponential Functions
After completing today’s lesson, you will be able to:
Identify an exponential function
Determine the domain & range of an exponential function
Evaluate an exponential function
Describe phenomena as representing exponential growth or decay.

3. Something to think about
Which would you prefer?
A million dollars today
Or a penny which doubles every day for the next 30 days
This is one of the reasons we study exponents, their properties, and their inverses

4. Exponential Functions
An exponential function is a function in terms of x, where x is an exponent in the function. It’s written in the form:
Where a is nonzero and b is positive and b≠1. The constant a is known as the initial value, and b is known as the base.

5. Examples of exponential functions and non-examples
Non-ex.s of Exp. Func.
How are these functions alike?
What makes an exponential function?

6. Which are exponential functions? Why?
a) c) b) d)

7. Computing values for x in exponential functions
e) Compute the exact value for f(x) without a calculator, where x=0.
Now you try it for x=2.

8. Use calculator to find the exp. Function from the table.
x f(x) /2 ¾ /8

9. Natural Base e
Put the function in your calculator and please observe the nature of the graph and its end behavior:

10. Natural base e
Since the end behavior approaches a constant, we can state:

11. Exponential Functions
Any exp. Function can be written as:
Where k is an appropriately chosen real number.

12. Exploration
Turn to page 280. Do Exploration 1, answer all the question in the activity. After you are done, please answer this question:
By looking at the graphs, what would each set of functions be: exponential growth, or decay?

13. Exponential Growth/Decay Functions
Exponential Growth, if and
ex.
Exponential Decay, if and

14. Review of Transformations: with Exponential functions
Where a is responsible for vertical stretch/shrink, and k is horizontal stretch/shrink.
Phase shifts occur horizontally from the constant h, and vertically from j.

15. Describe how g(x) will relate to f(x) for each example: