explain how an exponential function can be used to describe the teams in a tournament, algebra homework help

Writing in Math Use the information about Women’s basketball on page 518 to explain how an exponential function can be used to describe the teams in a tournament. Include an explanation of how you could use the equation y = 2x to determine the number of rounds of tournament play for 128 teams and an example of an inappropriate number of teams for a tournament.Find page 518 attached.

9-1Exponential Functions
GET READY for the Lesson
Main Ideas
2006 NCAA
• Graph exponential
functions.
Solve exponential
equations and
inequalities
New Vocabulary
exponential function
exponential growth
exponential decay
exponential equation
exponential inequality
The NCAA women’s
basketball tournament
2006 NCAA Women’s Tournament
begins with 64 teams
WWV
and consists of 6
UNC
Duke
rounds of play. The
MIDEAST UNC
Duke
EAST
winners of the first
round play against
Tennessee
Maryland
U Conn
each other in the
second round. The
Maryland
winners then move
from the Sweet
Utah
LSU
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*
Exponential Functions In an exponential function like y = 24, the base
is a constant, and the exponent is a variable. Let’s examine the graph
of y = 24
EXAMPLE
Graph an Exponential Function
Sketch the graph of y = 2*. Then state the function’s domain and range.
Make a table of values. Connect the points to sketch a smooth curve.
y
X
y = 24
y = 2
-3 2-3 = 1
8
12V7636
-2 2-2 = 1
-1 2-1 =3
0
2°= 1
I 2 = √2
Notice that
the domain
of y = 24
includes
irrational
numbers
such as V7.
2
As the value of
x decreases
the value of y
approaches 0.
1
2′ = 2
2
22 = 4
3
23 = 8
-2 -1 0
The domain is all real numbers, and the range is all positive numbers.