1. Exponential and Logarithmic Function
Lesson 2.4

2. Animated Exponential Function
Go to Spreadsheet of ax for a between 1/2 and 2

3. Exponential Function Definition: Where: b > 0 is a constant b ≠ 1
a is a constant
b < 1 a a
b > 1

4. Reminder Properties of exponents Note Theorem 2.8, pg 81
Properties of exponential functions

5. Example Consider equation: Solution:
Note that calculator will solve also

6. Logarithmic Functions
Inverse of exponential functions
Learn to translate back and forth from one form to the other

7. Examples
Try these:

8. Solutions
Check your work

9. Natural Log
Often the number e  … is used as the base for logarithms logex = ln x
This is the inverse of the exponential function with e as the base
Many computer languages use exp(x) for ex

10. Hint: base a will be base 10
Changing Bases
To change from base b to base a, use the formula shown:
Hint: base a will be base 10

11. Using Logarithms
Use to solve exponential equations

12. Application of Exponents
Exponential Growth
y = P0 ax periodic exponential growth
y = P0 ekt continuous exponential growth

13. Application of Exponents
Annually compounded interest A = (1 + r)t
Compounded n times per year
Continuous compounding A = P ert

14. Assignment
Lesson 2.4
Page 89
Exercises 1 – 39 odd, 55 – 69 odd