1. The space shuttle Challenger exploded 73 seconds into flight on January 28, The tragedy involved damage to o-rings , which were used to seal the connections between different sections of the shuttle engines.
msnbc.com
The number of o-rings damaged increases dramatically as Fahrenheit temperature falls. The function f(x) = (0.967)x -1 models the number of O-rings expected to fail when the temperature is x◦ F.
Mrs. McConaughy rex
Honors Algebra 2

2. 8.1 Exploring Exponential Models
Objectives:
To graph exponential functions
To evaluate exponential expressions
To use exponential functions as models for real-life problems
Mrs. McConaughy rex
Honors Algebra 2

3. Exponential Growth and Decay Models
Exponential Decay: f(x) = (1/2)x
Earlier, we studied graphs of basic exponential functions of the form f(x) = C(a)x,
where 0<a<1 represents ___________ and
a>1 represents _______________.
(0,1)
Exponential Growth: f(x) = (3)x
decay
(0,1)
growth
Mrs. McConaughy rex
Honors Algebra 2

4. Using Vertical Shift to Sketch Graphs
In this lesson, we will study vertical shifts, horizontal shifts and reflections of these two basic types of graphs.
EXAMPLE 1
Using Vertical Shift to Sketch Graphs
Sketch h(x) = 3x - 2
Sketch g(x) = (1/2)x + 1
(0,2)
(0,1)
(0,1)
(0,-1)
To sketch the graph of g, shift
the graph f(x) = (1/2)x up one unit.
To sketch the graph of h, shift
the graph f(x)= 3x down two units.
Mrs. McConaughy rex
Honors Algebra 2

5. Using Horizontal Shifts
EXAMPLE 2
Using Horizontal Shifts
Sketch g(x) = 2x + 3
Graph h(x) = 2x -2
Graph f(x) = 2x
y = 2x-2
y = 2x+3
y = 2x
To sketch the graph of h, shift
f(x) = 2x to the right 2 units.
To sketch the graph of g, shift
f(x) = 2x to the left 3 units.
Mrs. McConaughy rex
Honors Algebra 2

6. Reflections and Shifts
EXAMPLE 3 a.
Using Reflections and Shifts
Sketch the graph of g(x) = -(1/2)x + 4 :
g(x) = -(1/2)x + 4
f(x) = (1/2)x
h(x) = - (1/2)x
(0,1)
(0,3)
(0,-1)
Then shift the
Graph upward 4 units.
First, reflect the graph of
f(x) = (1/2)x in the
x axis.
Mrs. McConaughy rex
Honors Algebra 2

7. Reflections and Shifts
To sketch the graph of h, shift the graph of f(x) = 2x
2 units to the right. Then reflect the graph in the x-axis
and shift 2 units upward.
EXAMPLE 3b.
Using Reflections and Shifts
Sketch the graph of h(x) = - 2x :
(0,1)
h(x) = -2x-2 + 2
f(x) = 2x
Mrs. McConaughy rex
Honors Algebra 2

8. POWERS THAT HAVE IRRATIONAL EXPONENTS
EXAMPLE 4
Evaluating Powers that have Irrational Exponents
Use a calculator to evaluate the power.
Round the result to 3 decimal places.
a. 3√2
b. 3 - Π
Mrs. McConaughy rex
Honors Algebra 2

9. EXPONENTIAL DECAY MODEL
EXAMPLE 5
EXPONENTIAL DECAY MODEL
Suppose your parents purchased a new car for
$20, in If the value of the car depreciated
by 16% each year to 84% of its previous value, what was
the car worth in 2006? What will it be worth
in 2008?
Hint: Exponential Decay Model
V = Cat
= Initial Value (0.84)t
Mrs. McConaughy rex
Honors Algebra 2

10. Final Checks for Understanding
Compare the graphs of f(x) = 5x and
g(x) = 5x - 3.
Compare the graphs of f(x) = 3x and
g(x) = -3 x +2.
Use a calculator to evaluate 5 √3. Round the result to three decimal places.
Which function represents the value after x years of a delivery van that was purchased new for $17,500 and depreciates 11% every year?
A. y = -11 (17,500)x
B. y = 17,500 (0.11)x
C. y = 17,500 (.89)x
D. y = 17,500 (1.11)x
Mrs. McConaughy rex
Honors Algebra 2

11. Homework Assignment: Exponential Functions WS
Day 1: odd (use complete sentences); all (matching); 21, 25, 29, 33 (graphing); 40, 44 (calculator)
Mrs. McConaughy rex
Honors Algebra 2