Exponential and Logarithmic Functions (3 Questions), algebra homework help

Please show all work you did to solve the problems when you submit your work.This includes any calculations, diagrams, or graphs that helped yousolve it.

Writing in Math Use the information aboutWomen’s basketball on page 518 to explain how an exponential functioncan be used to describe the teams in a tournament. Include anexplanation of how you could use the equation y = 2xto determine the number of rounds of tournament play for 128 teams andan example of an inappropriate number of teams for a tournament. Page 518 is in the attachments Writing in Math Use the information aboutsound on page 529 to explain how a logarithmic scale can be used tomeasure sound. Include the relative intensities of a pin drop, awhisper, normal conversation, kitchen noise, and a jet engine written inscientific notation. Also include a plot of each of these relativeintensities on the scale below and an explanation as to why thelogarithmic scale might be preferred over the scale below. Page 529 is in the attachtments. 510
110)
UNC
Duke
The NCAA women’s
basketball tournament 2006 NCAA Women’s Tournament
begins with 64 teams
and consists of 6
UNC
Duke
rounds of play. The
MIDEAST
EAST
winners of the first
round play against
Tennessee
– Maryland
U Conn
each other in the
second round. The
Maryland
winners then move
Utah
LSU
from the Sweet
Duke
Sixteen to the Elite
WEST – Maryland
LSU MIDWEST
Eight to the Final
Four and finally to the
Maryland
Stanford
Championship Game.
The number of teams
y that compete in a tournament of x rounds is y = 2*
hy
Exponential Functions In an exponential function like y = 2, the base
is a constant, and the exponent is a variable. Let’s examine the graph
of y = 2
Page
5P8
Y
– 2″
7
EXAMPLE Graph an Exponential Function
Sketch the graph of y = 24. Then state the function’s domain and range.
Make a table of values. Connect the points to sketch a smooth curve.
y = 2
31
-3 2-3
277 – 6.3
-1 2-‘-}
Notice that
the domain
2° -1
of y = 2
21.v2
As the value of
includes
x decreases,
irrational
2’ = 2
the value of y
numbers
2 – 4
approaches 0.
such as V7.
2 = 8
–
2
Page
518
5
0
4
2
3
1
2
2 3
-3 -2 -1 0
The domain is all real numbers, and the range is all positive numbers.
wonential and Logarithmic Relations
High Sc
GUIK Tionue Lesson
so
Many scientific measurements have such an enormous range
of
possible values that it makes sense to write them as powers of 10 and
simply keep track of their exponents. For example, the loudness of
sound is measured in units called decibels. The graph shows the
relative intensities and decibel measures of common sounds.
Sound
101
M
Relative
Intensity
10
10
109
10
10
10
102
++
–
+
Decibels
0
20
40
60
80
100
120
pin
drop
whisper
(4 feet)
normal
conversation
noisy
kitchen
jet engine
The decibel measure of the loudness of a sound is the exponent or
logarithm of its relative intensity multiplied by 10.
pagro
29
6:56 PM
e
WE
6/19/2017
1
528 – 5251100
o
Ame
High Sc
Logarithmic functions and expressions to better understand what is
meant by a logarithm, consider the graph of y = 2* and its inverse. Since
exponential functions are one-to-one, the inverse of y = 2* exists and is
also a function. Recall that you can graph the inverse of a function by
interchanging the x- and y-values in the ordered pairs of the function.
Consider the exponential function y = 2* .
X= 2Y
У
y = 24
page
T I
-3
-3
(2.4)
y = x
-2
S-ll-I+|-IN
—lo -IT-In
-2.
1
-1
-1
(0.1)
Sza
(4.2) x = 2
0 1
1
0
0
(1.0)
x
1
| 2
2
1
As the value of y
decreases, the value
of x approaches o.
24
4
2
38
8
3
e
wa
6:56 PM
6/19/2017
1
528 – 5251100
o
Ame
High Sc
Logarithmic functions and expressions to better understand what is
meant by a logarithm, consider the graph of y = 2* and its inverse. Since
exponential functions are one-to-one, the inverse of y = 2* exists and is
also a function. Recall that you can graph the inverse of a function by
interchanging the x- and y-values in the ordered pairs of the function.
Consider the exponential function y = 2* .
X= 2Y
У
y = 24
page
T I
-3
-3
(2.4)
y = x
-2
S-ll-I+|-IN
—lo -IT-In
-2.
1
-1
-1
(0.1)
Sza
(4.2) x = 2
0 1
1
0
0
(1.0)
x
1
| 2
2
1
As the value of y
decreases, the value
of x approaches o.
24
4
2
38
8
3
e
wa
6:56 PM
6/19/2017