1. Algebra 2 9.1 Exponential Functions
y = abx
a = 0, b > 0 & b = 1

2. Characteristics of an Exponential Function
Function is continuous and one-to-one
Domain is the set of all real numbers
x-axis is an asymptote of the graph
Range is the set of all positive numbers if a > 0 and all negative numbers if a < 0
The graph contains the point (0, a)...y-intercept is a.

3. Exponential Growth & Decay
GROWTH: y = abx : a > 0 , b > 1
Example of Exponential Growth: y = 4(2)x
DECAY: y = abx : a > 0 , 0 < b < 1
Example of Exponential Decay: y = 7(½)x

4. Determine whether each function represents exponential growth or decay.
Ex. 1 y=(1/5)x
Decay
Ex. 2 y = 3(4)x
Growth
Ex. 3 y = 7(1.2)x
Ex. 4 y = (0.7)x
Decay
Ex. 5 y = ½(3)x
Growth
Ex. 6 y = 10(4/3)x

5. Properties of Exponents

6. Simplify these expressions using the properties of exponents

7. Exponential Equations
Equations in which variables occur as exponents.
b = 1, bx = by then x = y
Example: 2x = 28, then x = 8
Only works when both sides have the same bases

8. Solving exponential equations Example 10
Rewrite 81 with a base of 3
Since the bases are equal, set the exponents equal and solve
Solve for n

9. Solving exponential equations Example 11
Rewrite both sides with the same base of 2
Simplify by multiplying the powers
Set the exponents equal
Solve for x

10. Solve the following two equations.
Ex 12
Ex 13

11. Exponential Inequalities
If b > 1, then bx > by if and only if x > y, and bx < by if and only if x < y
For example: 5x < 54, then x < 4

12. Homework Assignment #56
p , 23-26, 31, 33, 42-46, 65, 66