how do i graph and use exponential growth and decay functions?
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• 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
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