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Exponential
Exponential Functions,
Functions,
Growth,
and Decay
Decay
Growth and
• How do we write and evaluate
exponential expressions to model growth
and decay situations?
HoltMcDougal
Algebra 2Algebra 2
Holt
Exponential Functions,
Growth, and Decay
Moore’s law, a rule used in the computer industry, states
that the number of transistors per integrated circuit (the
processing power) doubles every year. Beginning in the
early days of integrated circuits, the growth in capacity
may be approximated by this table.
Holt McDougal Algebra 2
Exponential Functions,
Growth, and Decay
Growth that doubles every year can be modeled by using
a function with a variable as an exponent. This function
is known as an exponential function. The parent
x
exponential function is f (x) = b , where the base b is a
constant and the exponent x is the independent variable.
Holt McDougal Algebra 2
Exponential Functions,
Growth, and Decay
The graph of the parent
x
function f(x) = 2 is shown.
The domain is all real
numbers and the range is
{y|y > 0}.
Holt McDougal Algebra 2
Exponential Functions,
Growth, and Decay
A function of the form f(x) = abx, with a > 0 and
b > 1, is an exponential growth function, which
increases as x increases. When 0 < b < 1, the function is
called an exponential decay function, which decreases
as x increases.
Holt McDougal Algebra 2
Exponential Functions,
Growth, and Decay
Remember!
In the function y = bx, y is a function of x because
the value of y depends on the value of x.
Remember!
Negative exponents indicate a reciprocal. For
example:
Holt McDougal Algebra 2
Exponential Functions,
Growth, and Decay
Recognizing Exponential Growth Functions
State whether the function represents exponential
growth or exponential decay.
x
1. f  x   3  4
1
exponential growth
2 . f  x   2  0.75
x
1
exponential decay
1
3. f  x   4 
 3
x
exponential decay
Holt McDougal Algebra 2
1
Exponential Functions,
Growth, and Decay
Recognizing Exponential Growth Functions
State whether the function represents exponential
growth or exponential decay.
x
exponential growth
6
4. f  x   4 
5
x
1
5. f  x   3 
4
x
f  x   34
Holt McDougal Algebra 2
1
exponential growth
1
Exponential Functions,
Growth, and Decay
Graphing Exponential Growth Functions
Graph the function.
x
6. y  2
x
y
 2 1/ 4
1 1/ 2
0 1
1 2
2 4
Holt McDougal Algebra 2
HA:
y0
Exponential Functions,
Growth, and Decay
Graphing Exponential Growth Functions
Graph the function.
x
7. y  3  2
x
y
2
1
0
1
2
3/ 4
3/ 2
3
6
 12
Holt McDougal Algebra 2
HA:
y0
Exponential Functions,
Growth, and Decay
Graphing Exponential Growth Functions
Graph the function.
1
8. y  2 
4
x
y
0 2
1 1/ 2
Holt McDougal Algebra 2
x
HA:
y0
Exponential Functions,
Growth, and Decay
Graphing Exponential Growth Functions
Graph the function.
2
9. y  5 
3
x
y
0 5
1  10 / 3
Holt McDougal Algebra 2
x
HA:
y0
Exponential Functions,
Growth, and Decay
Lesson 8.1 Practice A
Holt McDougal Algebra 2