Exponential and Logarithmic Functions

1. OPEN ENDED Give an example of a value of b for which y = bx represents exponential decay.
2. Writing in Math Use the information about Women’s basketball on page 498 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 = 2xto determine the number of rounds of tournament play for 128 teams and an example of an inappropriate number of teams for a tournament.
3. Writing in Math Use the information about sound on page 529 to explain how a logarithmic scale can be used to measure sound. Include the relative intensities of a pin drop, a whisper, normal conversation, kitchen noise, and a jet engine written in scientific notation. Also include a plot of each of these relative intensities on the scale below and an explanation as to why the logarithmic scale might be preferred over the scale below.

Exponential Functions
GET READY for the Lesson
2016 NCA
ste
The NCAA women’s
basketball tournament
2006 NCAA Women’s Tournament
begins with 64 teams
UNC
Duke
and consists of 6
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
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 = 24.
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*
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.
x y = 2
8
y = 2
-3
2-3 = 1
7
12v7
-2 2-2 = 1/2
6
5
1
2-1 = 1
0
20 = 1
Notice that
the domain
of y = 2
includes
irrational
numbers
1/2 27 = √2
As the value of
x decreases,
3