Definitions
Graphing Exponential Functions
Transformations
Word Problems
Solving Exponential Equations
100
An imaginary line that a graph approaches but does not meet.
Asymptote
100
What is the graph of the parent function
f(x)=(1/2)^x
100
What is a transformation of the function
f(x)=3^{x+3} - 2?
Horizontal Translation Left 3
OR
Vertical Translation Down 2
100
3x-4< 1/27
x < 1
100
Solve the equation
3^{x-7}=27^{2x}
x=-7/5
200
(0, 5) and (6, 320)
y = 5(2)x
200
What is the y - intercept of the function
f(x)=3(1/2)^x -1?
(0, 2)
200
Describe the transformations of the function
g(x)=4 \cdot 3^{x-2}+5
when compared to the function
f(x)=3^x?
Vertical Stretch by 4,
Horizontal Translation Right 2,
Vertical Translation Up 5
200
You buy a new computer for $2300. The value of the computer decreases by about 45% annually. Use
f(t)=2300(0.55)^t
to estimate the value after 2 years.
$695.75
200
Solve the following equation
3^{x-3}=3
x=4
300
Growth whose rate becomes more rapid in proportion to the growing total.
Exponential Growth
300
What is the domain of the function
f(x)=3(1/2)^x -1?
(-infty, infty)
300
What will the parent function
f(x)=9^x
be after a reflection across the x - axis?
f(x)=-9^x
300
You buy a new computer for $2300. The value of the computer decreases by about 45% annually. Write an exponential decay model for the value of the computer.
f(x)=2300(0.55)^x
300
Solve the following equation
4^{x+1}=1/64
x=-4
400
Decay whose rate becomes less rapid in proportion to the growing total.
Exponential Decay
400
What is the range of the function
f(x)=3(1/2)^x -1?
(-1, infty)
400
What will the parent function
f(x)=9^x
be after a vertical translation 5 units down?
f(x)=9^x-5
400
In the year 1995, about 20 million people used the internet. Between 1995 and 2001, the number of people who used the internet grew by about 75% per year. Which function best models the relationship between p, the number of people using the internet (in millions), and t, the number of years since 1995?
p(t)=20(1.75)^t
400
Classify the following as Exponential Growth, Exponential Decay, or Neither.
f(x)=6(6/5)^{-x}
Exponential Decay
500
(1/64)x-2=163x+1
4/9
500
What are the end behaviors of the function
f(x)= 3(1/2)^x -1?
As
x \to infty, f(x) \to -1
As
x \to -infty, f(x) \to infty
500
(1/27)2x+1 > (1/243)3x-2
x > 13/9
500
A box of paper clips begins with 270 clips. A person takes one-third of the clips and passes the box to a second person who takes one-third of the remaining clips. Another person then takes one-third of the remaining clips. How many clips remain when a fourth person receives the box?
10 Paper Clips
500
POPULATION In 2000, the world population was calculated to be 6,071,675,206. In 2008, it was 6,679,493,893. Write an exponential equation to model the growth of the world population over these 8 years. Round the base to the nearest thousandth.
y = 6,071,675,206(1.012)x