• How do I graph and use exponential growth and decay functions?

4.4 Graph Exponential Growth Functions

Exponential FunctionsFunctions of the form:

xaby Exponential growth if b > 1, where b is the growth factor.

Exponential decay if b < 1, where b is the decay factor.

4.4 Graph Exponential Growth Functions

Example 1 Graph Graph yy = = bbxx for for bb > 1 > 1

Graph y = 3x . Analyze the graph. Find the average rate of change over the interval 2 < x < 2.Step 1 Make a table of values.

x

y

2 1 0 1 2

9

1

3

11 3 9

Step 2 Plot the points from the table.

Step 3 Draw from left to right, a smooth curve that begins just ______ the x-axis, passes through the plotted points, and moves _________________.

aboveup to the right

4.4 Graph Exponential Growth Functions

Example 1 Graph Graph yy = = bbxx for for bb > 1 > 1

Graph y = 3x . Analyze the graph. Find the average rate of change over the interval 2 < x < 2.

Step 4 Examine the graph. The graph

intersects the y-axis at point _____. So

the y-intercept of y = 3x is __. You

can see from the graph that as the

value of x approaches the value

(0, 1)1

of the function approaches but never reaches ___. So the function has no zeros or x-intercepts. As the value of x approaches , the value of the function approaches _____. Also the function is increasing on the interval __________. Using the points (-2, 1/9), and (2, 9), the average rate of change over the interval -2 < x < 2 is _____, or about _____.

0

,

9/20 2.2

4.4 Graph Exponential Growth FunctionsCheckpoint. Complete the following exercises.Checkpoint. Complete the following exercises.

1. Graph y = 2x and find the average rate of change over the interval 2 < x < 2.

x

y

2 1 0 1 2

4

1

2

11 2 4

m 25.04

22 3.75

4

400

375

15

16

4.4 Graph Exponential Growth Functions

Example 2 Graph Graph yy = = ababxx for for bb > 1 > 1

Then, from left to right, draw a curve that begins just ______ the x-axis, passes through the two points, and moves _________________.

above

up to the right

.64

1function Graph the xy

Solution

Plot and ____,0 . ,1 ____4

1

2

3

Then translate the graph ____________ and _____________.

4.4 Graph Exponential Growth Functions

Example 3 Graph Graph yy = = ababx – h x – h + + kk for for bb > 1 > 1

.232Graph 2 xyState the domain and range.SolutionBegin by sketching the graph of

y = 2. 3x , which passes through ( 0, ___) and ( 1, ___). 2

right 2 units down 2 units

6

The graph’s asymptote is the line _____________.2yThe domain is all real __________,numbersand the range is __________.2y

4.4 Graph Exponential Growth FunctionsCheckpoint. Complete the following exercises.Checkpoint. Complete the following exercises.

2. Graph the function.342 1 xy

State the domain and range.xy 42

,0 2 ,1 8Translation:left 1 unit

down 3 units

Domain: All real numbers Range: 3yAsymptote: 3y

4.4 Graph Exponential Growth Functions

Pg. 134, 4.4 #1-12