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