Exploring Exponential
Functions
Exponential Function
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The independent variable (x) is an
exponent.
f(x) = a • bx
“a” cannot be zero, “b” cannot be one
and must be positive.
Exponential Functions
y  ab
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x
“a” is the initial amount or the amount
with which you start.
“b” is the growth or decay factor
“x” is the number of times it grows or
decays.
Example 1
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Suppose that two mice live in a
farmhouse. If the number of mice
quadruples every 3 months, how many
mice will be in the house after 2 years?
Make a table.
Example 1
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How many mice at
the beginning (initial
amount)?
How many mice
after 3 months?
How many mice
after 6 months?
How many mice
after 9 months?
Months
0
3
6
9
Mice
2
8
32
128
Example 1
y  ab
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y  2 4
8
x
Replace “a” with the initial amount (2
mice).
Replace “b” with what is happening to
the number of mice (Being multiplied by
4).
Replace “x” with the number of 4
month periods (8).
Write an exponential function
for…
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There are 200 cells in a jar. The number of
cells triples every hour.
y = 200 • 3x
There are 5 cats on an island. The number of
cats doubles every three weeks.
y = 5 • 2x
There is $800 in a savings account. The
amount doubles every 8 years.
y = 800 • 2x
Evaluate each exponential
function
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y = 3x for x = 1, 2,
and 4
y = 2.5x for x = 2, 3
and 4
 2
y 
 5
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x
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for x  1, 2, and 5
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{3, 9, 81}
{6.25, 15.625,
39.0625}
(0.4, 0.16, 0.01024}
Graph y = 5(2)x
Plug it into y=.
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Go to the table.
Pick points that
will fit on the grid.
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Graph y = 3(1/2)x
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