Graphing Exponential Equations
Growth
  Graphing Exponential Equations
Two types of exponential equations
Decay
With a plant, the leaves grow in the upward (+y)
direction and the roots grow in the downward (-y)
direction.
With an exponential function, growth is anythingmoving away from a horizontal axis in either theupward or downward direction. The graph gets morevertical. This represents an increase over time.
  Graphing Exponential Equations
Growth
x
With radioactive material, the element decreases in its amount present
over time.
With an exponential function, decay is anything
moving towards the horizontal axis from either theupward or downward direction. The graph gets morehorizontal. This represents a decrease over time.

  Graphing Exponential Equations
Decay
x
0
2
-2
4
-4
General form when there is an offset (h, k)

y = a•(b)x-h + k
b: is the base and determines if the function grows or decays
0 < b < 1
  Graphing Exponential Equations
Decay
Growth
y = a•(b)x
b > 1
Commom Form
General form when there is an offset (h, k)

Identifying exponentials using 3 characteristics:
1. What is "k"?

2. What is "b"?

3. What is "a"?
y = a•(b)x-h + k
"a" is the multiplier.
"b" is the base.
"k" is the location
of the asymptote.
Graphing Exponential Equations
The base indicates growth or decay.Growth: b > 1Decay: 0 < b < 1

Exponential functions are asymptotic

with a horizontal line. This means

there is a horizontal line that the

function gets close to but never crosses.

The multiplier indicates if the function is drawn
above the asymptote or below the asymptote.+a drawn above-a drawn below
y = a•(b)x
Commom Form
Growth
Growth: b > 1
Growth: b > 1
+a drawn above
-a drawn below
Graphing Exponential Equations
General form when there is an offset (h, k)

y = a•(b)x-h + k
k is the horizontal asymptote
+a drawn above
Decay: b < 1
Decay: b < 1
-a drawn below
Decay
Graphing Exponential Equations
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Look at the graph, when x = 0
y = -1/2 so a = 
General Form: y = a•(b)x-h + k
Asymptote is at k = 
This is drawn below the asymptote
so a is
This is growth so b
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Graphing Exponential Equations
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Look at the graph, when x = 0y = 4 so a = 
General Form: y = a•(b)x-h + k
Asymptote is at k = 
This is drawn above the asymptote
so a is
This is decay so b
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Graphing Exponential Equations
This is drawn above the asymptote
so a is
Look at the graph,when x = 0, y = 2.5so a = 0.5
Asymptote is at k = 
General Form: y = a•(b)x-h + k
This is growth so b
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1
Graphing Exponential Equations
This is drawn above the asymptote
so a is
Look at the graph,when x = 0, y = 7so a = 5
Asymptote is at k = 
General Form: y = a•(b)x-h + k
This is decay so b
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1
Graphing Exponential Equations
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Look at the graph, when x = 0y = -3 so a = 
General Form: y = a•(b)x-h + k
Asymptote is at k = 
This is drawn below the asymptote
so a is
This is growth so b
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1
Graphing Exponential Equations
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Look at the graph, when x = 0y = -4 so a = 
General Form: y = a•(b)x-h + k
Asymptote is at k = 
This is drawn below the asymptote
so a is
This is growth so b
&#124;
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1
Graphing Exponential Equations
This is drawn above the asymptote
so a is
Look at the graph,when x = 0, y = 4so a = 
Asymptote is at k = 
General Form: y = a•(b)x-h + k
This is growth so b
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1
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Graphing Exponential Equations
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Look at the graph, when x = 0y = -1/3 so a = 
General Form: y = a•(b)x-h + k
Asymptote is at k = 
This is drawn below the asymptote
so a is
This is growth so b
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1
Graphing Exponential Equations
This is drawn above the asymptote
so a is
Look at the graph,when x = 0, y = 2so a = 4
Asymptote is at k = 
General Form: y = a•(b)x-h + k
This is decay so b
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1
Graphing Exponential Equations
This is drawn above the asymptote
so a is
Look at the graph,when x = 0, y = 2so a = 
Asymptote is at k = 
General Form: y = a•(b)x-h + k
This is growth so b
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1
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Graphing Exponential Equations
This is drawn below the asymptote
so a is
Look at the graph,when x = 0, y = -4so a = -4
Asymptote is at k = 
General Form: y = a•(b)x-h + k
This is decay so b
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1
Graphing Exponential Equations
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Look at the graph, when x = 0y = -2 so a = 
General Form: y = a•(b)x-h + k
Asymptote is at k = 
This is drawn below the asymptote
so a is
This is growth so b
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1
Graphing Exponential Equations
This is drawn below the asymptote
so a is
Look at the graph,when x = 0, y = -1/4so a = -1/4
Asymptote is at k = 
General Form: y = a•(b)x-h + k
This is decay so b
1
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Graphing Exponential Equations
This is drawn above the asymptote
so a is
Look at the graph,when x = 0, y = 3so a = 
Asymptote is at k = 
General Form: y = a•(b)x-h + k
This is growth so b
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1
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Graphing Exponential Equations
This is drawn above the asymptote
so a is
Look at the graph,when x = 0, y = 4so a = 2
Asymptote is at k = 
General Form: y = a•(b)x-h + k
This is decay so b
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1
Graphing Exponential Equations
This is drawn above the asymptote
so a is
Look at the graph,when x = 0, y = 18so a = 
Asymptote is at k = 
General Form: y = a•(b)x-h + k
This is growth so b
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1
Graphing Exponential Equations
This is drawn below the asymptote
so a is
Look at the graph,when x = 0,y = 1.75so a = -0.25
Asymptote is at k = 
General Form: y = a•(b)x-h + k
This is decay so b
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1
Graphing Exponential Equations
This is drawn above the asymptote
so a is
Look at the graph,when x = 0, y = 8so a = 
Asymptote is at k = 
General Form: y = a•(b)x-h + k
This is growth so b
1
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Graphing Exponential Equations
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Look at the graph, when x = 0y = 1/2 so a = 
General Form: y = a•(b)x-h + k
Asymptote is at k = 
This is drawn above the asymptote
so a is
This is decay so b
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1
Graphing Exponential Equations
Look at the graph,
when x = 0y = -2.25so a = 
General Form: y = a•(b)x-h + k
Asymptote is at k = 
This is drawn below the asymptote
so a is
This is growth so b
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1
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