More Related Content Similar to Lecture 10 section 4.1 and 4.2 exponential functions Similar to Lecture 10 section 4.1 and 4.2 exponential functions (20) More from njit-ronbrown (20) 2. The term 27
is called a power. If a number is in exponential form, the
exponent represents how many times the base is to be used as a factor.
7
Exponent
Base
2
3. 3
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RULES OF EXPONENTS
Let a, b, x, and y be real numbers with a > 0
and b > 0. Then
,x y x y
a a a +
× =
,
x
x y
y
a
a
a
−
=
( ) ,
x x x
ab a b=
( ) ,
yx xy
a a=
0
1,a =
1 1
.
x
x
x
a
a a
−
= = ÷
10. 10
© 2010 Pearson Education, Inc. All rights reserved
EXAMPLE 6 Sketching Graphs
Use transformations to sketch the graph of each
function.
( ) 3 4x
f x = −a.
State the domain and range of each function and
the horizontal asymptote of its graph.
( ) 1
3x
f x +
=b.
( ) 3x
f x = −c. ( ) 3 2x
f x = − +d.
13. Note that the graph of ex
is between 2x
and 3x
,
because 2<e<3. In the first quadrant, 2x
<ex
<3x
;
in the second quadrant, 3x
<ex
<2x
.
All 3 graphs pass through (0,1).
15. ( )
4
3 -1 2 1
3
Solve each exponential equation.
1
(a) 2 32 (b)x x x
x
e e
e
− −
= = ×
17. 17
© 2010 Pearson Education, Inc. All rights reserved
EXAMPLE 8 Bacterial Growth
A technician to the French microbiologist Louis
Pasteur noticed that a certain culture of bacteria
in milk doubles every hour. If the bacteria count
B(t) is modeled by the equation
B t( ) = 2000 ×2t
,
a. the initial number of bacteria,
b. the number of bacteria after 10 hours; and
c. the time when the number of bacteria will be
32,000.
with t in hours, find
20. Find the amount A that results from investing a principal P of
$2000 at an annual rate r of 12% compounded continuously for
a time t of 3 years.
