Transcript Exponential Functions are functions which can be represented by graphs similar to the graph on the right.

Exponential
Functions are
functions which
can be
represented by
graphs similar
to the graph on
the right
All base exponential functions are similar because
they all go through the point (0,1), regardless of
the size of their base number
Exponential Functions are written in the form:
y=
a= constant
x
ab
b = base
x = variable
When working with exponential equations,
the Laws of Exponents still hold true
1
3
1
3
1 1
3
3  9
2
When solving exponential equations, it is
important to have both sides of the equation
set to the same base
 
25 125 5
x
2 x
5 
3
5  5  2x  3  x  1.5
2x
3
Yellow = 4x
Green = ex
Black = 3x
Red = 2x
As you could see in the graph, the larger the
base, the faster the function increased
If we place a negative sign in front of the x,
the graphs will be reflected(flipped) across
the y-axis
Yellow = 4-x
Green = e-x
Black = 3-x
Red = 2-x
By using Microsoft Excel, we can make a table of
values and a graph of the data
X-Value Y-Value
-5
0.01
-4
0.02
-3
0.05
-2
0.14
-1
0.37
0
1.00
1
2.72
2
7.39
3
20.09
4
54.60
5
148.41
y = ex
160.00
140.00
120.00
100.00
80.00
60.00
40.00
20.00
0.00
We can also use Maple 7 to plot exponential graphs
> plot (exp(x),x=-5..5);
The previous pages show what exponential growth
looks like as a curve, but what happens in real life.
You start with one item which replicates continuously.
Homework:
Pages ?
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