1 Modeling The function
y
=
a
b
x
,
y equals , eh b to the x , comma
a
>
0
,
eh greater than 0 comma
b
>
1
,
b greater than 1 comma models exponential growth.
y
=
a
b
x
y equals , eh b to the x models exponential decay if
0
<
b
<
1
.
0 less than b less than 1 .
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Exponential Models (Lesson 7-1)
The population P is 1000 at the start. In each time period,
•
P
grows by 5%.
P
=
1000
(
1.05
)
t
p equals , 1000 . open , 1.05 , close to the t •
P
shrinks by 5%.
P
=
1000
(
0.95
)
t
p equals , 1000 . open , 0.95 , close to the t
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Properties of Logarithms (Lesson 7-4)
b
a
b
c
=
b
a
+
c
log
b
m
n
=
log
b
m
+
log
b
n
b
a
b
c
=
b
a
−
c
log
b
m
n
=
log
b
m
−
log
b
n
log
b
m
n
=
n
log
b
m
log
n
m
=
log
b
m
log
b
n
table with 6 rows and 2 columns , row1 column 1 , b to the eh , b to the c , column 2 equals , b super eh plus end super . to the c , row2 column 1 , log base b , m n , column 2 equals , log base b , m plus , log base b , n , row3 column 1 , fraction b to the eh , over b to the c end fraction , column 2 equals . b super eh minus c end super , row4 column 1 , log base b . m over n , column 2 equals , log base b , m minus , log base b , n , row5 column 1 , log base b . m to the n , column 2 equals n , log base b , m , row6 column 1 , log base n , m , column 2 equals . fraction log base b , m , over log base b , n end fraction , end table
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3 Function The exponential function
y
=
b
x
y equals , b to the x and the logarithmic function
y
=
y equals
log
b
x
log base b , x are inverse functions. |
Logarithmic Functions as Inverses (Lesson 7-3)
Image Long Description
•
y
=
2
x
y equals , 2 to the x
•
y
=
log
2
x
y equals , log base 2 , x
•
y
=
2
x
−
1
y equals . 2 super x minus 1 end super
•
y
=
(
log
2
x
)
+
1
y equals open , log base 2 , x close plus 1
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Exponential and Natural Logarithm Equations (Lessons 7-5 and 7-6)
e
x
+
3
=
4
e super x plus 3 end super . equals 4
e
x
·
e
3
=
4
e to the x , middle dot , e cubed , equals 4 or
x + 3 = ln 4
e
x
=
4
e
3
x
=
l
n
4
e
3
table with 2 rows and 2 columns , row1 column 1 , e to the x , column 2 equals , fraction 4 , over e cubed end fraction , row2 column 1 , x , column 2 equals l n , fraction 4 , over e cubed end fraction , end table
x
=
(
ln
4
)
−
3
x equals open ln 4 close minus 3
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