1. Exponential Functions and Their Graphs Presented by the best teacher in the world: Mr. Peter Richard

2. The Exponential Function
y = abx
b is the base: GROWTH
It must be greater than 0
It cannot equal 1.
x can be any real number .

3. Identify Exponential Functions
Which of the following are exponential functions?
y = 3x
y = x3
yes no
y = 2(7)x
y = 2(-7)x
yes no

4. Exponential Factors
If the factor b is greater than 1, then we call the relationship exponential growth.
If the factor b is less than 1, we call the relationship exponential decay.

5. Determine Whether Growth or Decay
State whether the function is an exponential growth or exponential decay function. (Look at the “b” Value. Is it more or less than one?)
decay
growth
decay
decay
growth

6. GRAPHING EXPONENTIAL DECAY MODELS
EXPONENTIAL GROWTH MODEL
EXPONENTIAL DECAY MODEL
y = C (1 + r)t
y = C (1 – r)t
An exponential model y = a • b t represents exponential growth if b > 1 and exponential decay if 0 < b < 1.
1 + r > 1
0 < 1 – r < 1

7. The value of f(x) = 3x when x = 2 is9
The value of f(x) = 3x when x = –2 is
f(–2) = 3–2 =
The value of g(x) = 0.5x when x = 4 is
g(4) = 0.54 =
0.0625
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8. Example: Sketch the graph of f(x) = 2x. x f(x) (x, f(x))y x
f(x)
(x, f(x)) -2
(-2, ¼) -1
(-1, ½) 1
(0, 1) 2
(1, 2) 4
(2, 4) 4 2 x –2 2
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9. Example: Sketch the graph of g(x) = 2x – 1. State the domain and range.y
f(x) = 2x
The graph of this function is a vertical translation of the graph of f(x) = 2x down one unit . 4 2
Domain: (–, ) x
y = –1
Range: (–1, )
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10. Example: Sketch the graph of g(x) = 2-x. State the domain and range.y
f(x) = 2x
The graph of this function is a reflection the graph of f(x) = 2x in the y-axis. 4
Domain: (–, ) x –2 2
Range: (0, )
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11. The irrational number e, where e  2.718281828…
is used in applications involving growth and decay.
Using techniques of calculus, it can be shown that
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12. The Graph of f(x) = ex x f(x) -2 0.14 -1 0.38 1 2.72 2 7.39 y x 6 4 21
2.72 2
7.39 6 4 2 x –2 2
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13. Quiz and Homework Quiz: Page 435 # 16, 18, 20, 24, 26 Homework # 17, 19, 21, 27, 29
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