1. Evaluate each expression for the given value of x.
Teacher
Algebra 3
Warm-Up 5.1
Evaluate each expression for the given value of x.
2x for x = x+1 for x = 2
x3x+4 for x = for x = 0
23 = = 64
(1)7 = ( ½ )0 = 1

2. Objective: The students should be able to graph exponential equations.
Teacher
Algebra 3
Lesson 5.1
Objective: The students should be able to graph exponential equations.
Standards: C; S

3. Linear Equation  Graph is straight line
Quadratic Equation  Graph is a parabola
 This lesson we will look at Exponential Equations

4. A function with the general form y = abx
Teacher
Exponential Function
A function with the general form y = abx
(x is a real number, b > 0, a≠0, b≠0)
- The variable is in the Exponent

5. Take a look at the exponential function y = 2x
In this function the variable is the exponent
Graph of y = 2x

6. Graphing Exponential Functions
Teacher
Graphing Exponential Functions
 Make a table of values using negative and positive numbers for x
 Plot the points
Asymptote: A line that a graph will approach but never intersect.

7. 1. Graph y = 4(2)x x y -3 -2 -1 1 2 3
0.5 1 2 4 8 16 32
Horizontal Asymptote: y = 0
(the graph gets very close but never touches)

8. Teacher
2. Graph y = 3x
Make a Table of Values x y -3 -2 -1 1 2 3
0.037
0.111
0.333 1 3 9 27
Horizontal Asymptote: y = 0
(the graph gets very close but never touches)

9. 3. Graph x y -3 -2 -1 1 2 3
108 36 12 4
1.33
.444
.148

10. 4. Graph: x y -3 -2 -1 1 2 3
-0.016
-0.08
-0.4 -2
-10
-50
-250

11.  b is called the growth factor
Teacher
y = abx
Exponential Growth
 The exponential function will model exponential growth when b > 1 and a > 0
 b is called the growth factor
 The Graph will increase from left to right
 Look for words like Increase or Appreciation

12.  b is then called the decay factor
Teacher
y = abx
Exponential Decay
 The exponential function will model exponential decay when 0 < b < 1 and a > 0
 b is then called the decay factor
 Graph will decrease from left to right
 Look for words like Decrease or Depreciation

13. y = 1000(0.12)x y = 0.2(5)x y = 16(½)x Decay  b < 1 4. y = 8(3.5)x
Teacher
Examples: Without graphing determine whether each function represents exponential growth or decay. Recall: y = abx
y = 1000(0.12)x
y = 0.2(5)x
y = 16(½)x
y = 8(3.5)x
Decay  b < 1
Growth  b >1
Growth  b > 1

14. On your Own: Graph the following. y = 10(0.1)x-3 -2 -1 1 2 3
10000
1000
100 10 1
0.1
0.01

15. Homework
Worksheet 5.1