Overview
Exponential Graphs
This presentation will include:
I
Exponential equations;
I
The Learning Centre
1
Exponential equations
Exponential equations: Growth
Your graph should look something like the one below.
Let us look at the number of ancestors a person has.
Grandparent
Grandparent
6
2
y
Grandparent
6
20
18
16
14
12
10
8
6
4
2
Grandparent
6
6
?
?
Parent
Parent
6
6
y = 2x
?
x
You
1
We could continue this indefinitely, but let us instead look at this
information in a table.
Generations back (x)
Number of ancestors (y)
0
1
1
2
2
4
3
8
4
16
5
32
6
64
7
128
8
256
3
2
3
4
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The equation to this curve is y = 2x . We call this type of graph an
exponential growth curve and often use it in population growth
studies.
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The name refers to the position of the x in the exponent of the
equation.
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As the number of generations back (x) increases, the number of
ancestors (y) becomes greater and greater. The curve grows steeper
and steeper.
4
Exponential growth graph:
Another example
Exponential equations: Decay
y
25
y = ex
20
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Consider the equation to the curve y = 2−x
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We call this type of graph an exponential decay curve.
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This time as x takes on more positive values, the curve comes
closer and closer to the x-axis but never touches it.
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Exponential decay curves occur in such areas as science when
we talk about radio active decay and in business when we talk
about depreciation.
15
10
5
y-intercept (0, 1)
x
−3
−2
−1
1
2
3
4
5
Exponential decay Graph
y
10
8
6
4
y-intercept (0, 1)
2
y = 2−x
x
−3
−2
−1
1
2
3
4
7
6