1. Section 4.1 Exponential Functions
Chapter 4 – Exponential and Logarithmic Functions
Section 4.1 Exponential Functions
4.1 - Exponential Functions

2. Exponential Functions
What is an exponential function?
An exponential function has its variable in the exponent.
It may be used to model rapidly increasing or decreasing situations such as population growth, growth of epidemics, radioactive decay, cooling or heating of objects, etc.
4.1 - Exponential Functions

3. Review – Laws of Exponents
Simplify the following:
4.1 - Exponential Functions

4. 4.1 - Exponential Functions
Evaluating
Answer the question below.
In college, we study large volumes of information that, unfortunately, we do not often retain for very long. The function
describes the percentage of information that a person can be expected to remember x weeks after learning it.
4.1 - Exponential Functions

5. 4.1 - Exponential Functions
Evaluating
1.) Let x = 0 and give the value of f (0).
f (0)= 100
2.) Let x = 1 and determine the value of f (1)
accurate to the nearest ten-thousandth.
f (1)=
3.) Let x = 52 and determine the value of f (52) accurate to the nearest thousandth.
f (52)= 20
4.1 - Exponential Functions

6. Exponential Functions
The exponential function with base a is defined for all real numbers x by
where a > 0 and a  1.
4.1 - Exponential Functions

7. Exponential Functions
What does an exponential function look like?
What is its domain and range?
Does it increase or decrease or both?
Does it have vertical or horizontal asymptotes?
4.1 - Exponential Functions

8. Exponential Functions
What does an exponential function look like?
What is its domain and range?
Does it increase or decrease or both?
Does it have vertical or horizontal asymptotes?
4.1 - Exponential Functions

9. Graphs of Exponential Functions

10. Transformations of Functions
We will now see how to graph certain functions by looking at the basic graphs of exponential functions and applying the shifting and reflecting transformations.
4.1 - Exponential Functions

11. 4.1 - Exponential Functions
Example
Use the graph of to sketch the graph of each function.
4.1 - Exponential Functions

12. 4.1 - Exponential Functions
Example – pg. 308 # 19 & 20
Find the exponential function f (x) = ax whose graph is given.
4.1 - Exponential Functions

13. 4.1 - Exponential Functions
Application
Exponential functions occur in calculating compound interest.
4.1 - Exponential Functions

14. Compounding – Key Words
Annual 1
Semiannual 2
Quarterly 4
Monthly 12
Daily
365
4.1 - Exponential Functions

15. 4.1 - Exponential Functions
Example – pg. 309 # 52
If $ is invested at an interest rate of 2.5%, compounded daily, find the value of the investment after the given amount of years.
2 years
3 years
6 years
4.1 - Exponential Functions

16. 4.1 - Exponential Functions
Example – pg. 309 #56
Find the present value of $100,000 if interest is paid at a rate of 8% per year, compounded monthly, for 5 years.
4.1 - Exponential Functions