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Notes Over 5.1Graphing Exponential Functions
xxf 2 .1 Graph both functions on the same graph.
x y
2 4/11
012
2/1124
xxg 4x y
2 16/11
012
4/11416
A larger base makes it increase faster.
Notes Over 5.1Graphing Exponential Functions
xxF 2 .2Graph both functions on the same graph.
x y
2 41
012
212/14/1
xxG 4
x y
2 161
012
414/116/1
A larger base makes it decrease faster.
Notes Over 5.1Graphing Exponential Functions
3. Compare the graphs both functions in Example 1 and 2.
xxF 2 f x Reflects over the y-axis
xxG 4 g x Reflects over the y-axis
1, of graphs aay x 1, of graphs aay x
Domain:
Range:y-int:
Inc/Dec:
asymp:
Contin:
, , ,0 ,0
1 1increasing decreasing
0y 0ycontinuous continuous
Notes Over 5.1Transformations of Exponential Functions
Graph the transformation of the function.
43 .4 2 xxf 3Graph xy Move curve 2 units to the right
Domain: All real numbers
Range: 4y
and 4 units up
Asymptote: 4y
35
34
x
xg
Notes Over 5.1Transformations of Exponential Functions
Use the graph of f to describe the transformation that yields the graph of g.
,5
3 .5
x
xf
move curve 4 units to the leftand 3 units down
Reflect over x-axis,
2 .7 e
Notes Over 5.1Evaluating the Natural Exponential Function
Use a calculator to evaluate each expression.
1 .6 e...7182818.2 ...1353353.0
Notes Over 5.1Graphing Natural Exponential Functions
xexf 5.02 .8 Graph both functions on the same graph.
x y
2 736.1
012
213.12297.3437.5
xexg 5.02
x y
2 437.51
012
297.32213.1736.
The first is increasing while the second is decreasing.
Notes Over 5.1Modeling Exponential Growth
Compound Interestnt
n
rPA
1
P is initial amountr is the growth rate t is the time period
n is the number of times per year
Continuous Compounding
rtPeAP is initial amount
r is the growth ratet is the time period
Notes Over 5.1Modeling Exponential Growth
tn
n
rPA
1
9. A customer purchases a television set for $800 using a credit card. The interest is charged on any unpaid balance at a rate of 18% per year compounded monthly. If the customer makes no payment for one year, how much is owed at the end of the year?
800
The customer would owe $956.49.
12015.1800A
18.1
49.95612
12
compounded monthly
$800
18%one year
Notes Over 5.1Modeling Exponential Growth
trePA
10. 15 monkeys were released into a reserve. If they increase at a rate of 20% compounded continuously, how many monkeys will be in the reserve in 5 years, 10 years, and 15 years?
15115eA
5
41
2.
compounded continuously15
20%5 years
215eA 111315eA 301
1015
Notes Over 5.1