Holt McDougal Algebra 2

Exponential Functions, Growth, and DecayExponential Functions, Growth and Decay

Holt Algebra 2Holt McDougal Algebra 2

• How do we write and evaluate exponential expressions to model growth and decay situations?

Holt McDougal Algebra 2

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 exponential function is f (x) = bx, 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 function f(x) = 2x 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

Negative exponents indicate a reciprocal. For example:

Remember!

In the function y = bx, y is a function of x because the value of y depends on the value of x.

Remember!

Holt McDougal Algebra 2

Exponential Functions, Growth, and DecayRecognizing Exponential Growth Functions

xxf 43 .1

State whether the function represents exponential growth or exponential decay.

4 1exponential growth

xxf 75.02 .2 75.0 1exponential decay

x

xf

3

14 .3

3

11

exponential decay

Holt McDougal Algebra 2

Exponential Functions, Growth, and DecayRecognizing Exponential Growth Functions

State whether the function represents exponential growth or exponential decay.

xxf 43

x

xf

5

64 .4

5

61

exponential growth

x

xf

4

13 .5

4 1

exponential growth

Holt McDougal Algebra 2

Exponential Functions, Growth, and DecayGraphing Exponential Growth Functions

xy 2 .6 Graph the function.

x y

2 4/11012

2/1124

HA: 0y

Holt McDougal Algebra 2

Exponential Functions, Growth, and DecayGraphing Exponential Growth Functions

Graph the function.xy 23 .7

x y

2 4/31012

2/336

12

HA: 0y

Holt McDougal Algebra 2

Exponential Functions, Growth, and DecayGraphing Exponential Growth Functions

Graph the function.x

y

4

12 .8

x y

0 21 2/1

HA: 0y

Holt McDougal Algebra 2

Exponential Functions, Growth, and DecayGraphing Exponential Growth Functions

Graph the function.x

y

3

25 .9

x y

0 51 3/10

HA: 0y

Holt McDougal Algebra 2

Exponential Functions, Growth, and Decay

Lesson 8.1 Practice A