Exponential FunctionsExponential Functions

Exponential GrowthExponential Decay

y

x

Exponential FunctionExponential Function

b represents the “beginning value”b is also the y-intercept

g represents the growth rate– As g increases, the exponential curve gets steeper.– As g decreases, the exponential curve flattens

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Exponential GrowthExponential Growth

For the exponential function to be exponential growth, “g > 1”.

There is a horizontal asymptote at y = k.Domain: is all real numbers.Range:

– If b > 0, then the range is y > k.– If b < 0, then the range is y < k.

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Exponential DecayExponential Decay

For the exponential function to be exponential decay, “g < 1”.

There is a horizontal asymptote at y = k.Domain: is all real numbers.Range:

– If b > 0, then the range is y > k.– If b < 0, then the range is y < k.

xbgy

Graph Graph by creating a by creating a table of values table of values

xy 21

y

x

x y

-4

-2

0

1

2

3

0.0625

0.25

1

2

4

8

Graph Graph by creating a by creating a

table of values.table of values.

x

y

211

y

x

x y

-2

-1

0

2

4

6

4

2

1

0.250.0625

0.0156

Graph Graph by creating a by creating a table of values.table of values.

xy 21

x y

-2

-1

0

1

2

3

y

x

-0.25-0.5

-1

-2-4

-8

Graph Graph by creating a by creating a

table of values.table of values.

x

y

211

x y

-3

-2

-1

0

1

2

y

x

-8

-4

-2

-1

-0.5-0.25

General Graph of General Graph of Exponential GrowthExponential Growth

kbgy hx

y

x

h shifts the curve Right/Left

k shifts the curve Up/Down

Graph the CurveGraph the Curvey

x

4232

2

x

y

2326

1

x

y

Graph the CurveGraph the Curvey

x